An Application of Alternative Weighting Matrix Collapsing Approaches for Improving Sample Estimates
|
|
- Juniper Casey
- 6 years ago
- Views:
Transcription
1 Secton on Survey Research Methods An Applcaton of Alternatve Weghtng Matrx Collapsng Approaches for Improvng Sample Estmates Lnda Tompkns 1, Jay J. Km 2 1 Centers for Dsease Control and Preventon, atonal Center for Statstcs, 3311 Toledo Road, Room 3115, Hyattsvlle, MD, Centers for Dsease Control and Preventon, atonal Center for Statstcs, 3311 Toledo Road, Room 3111, Hyattsvlle, MD, Abstract When creatng sample weghts, most U.S. government agences combne small race groups such as the Amercan Indans and Asans wth Whtes dsregardng the dfferent coverage ratos of the groups. Ths paper examnes ths methodology usng the 2003 atonal Intervew Survey (HIS) data of the atonal Center for Statstcs (CHS) and reports the effect on the sample weghts and estmates, specfcally for Whtes, Amercan Indans (AI) and Asans. Two alternatve weghtng approaches wll be used n an effort to reduce the bas. KEY WORDS: coverage rato, sample weghtng, cell collapsng. 1. Introducton Before fnal weghts are developed for survey data, a poststratfcaton (rato or ntal adjustment) factor (PSF) s calculated for each cell (row or column) of a weghtng matrx and appled to the cell. However, for some cells, poststratfcaton factors cannot be computed. For example, f the sample count s zero for a cell, t s mpossble to calculate the PSF because the denomnator of the nvolved fracton s zero. Also f the raw sample count for a fracton s small, the fracton would be consdered unstable. Because of these occurrences n many surveys, cells are checked as to whether they have enough raw sample cases to stand by themselves.. Addtonally, for most surveys, the cells are checked to see whether ts PSF les wthn an acceptable range. Ths rato crteron assures that the fnal weghts are not too large or too small. It should be noted that very large or small weghts can nflate the varance of estmates. If a cell fals ether of the above tests, t s combned wth another cell. The cell collapsng strategy descrbed above has merts. However, Km (2004) rased a potental problem of combnng cells whch are dfferent n coverage ratos. Let be the control count for cell, ˆ the ntally weghted sample count for cell, =1, 2 and f ˆ =, =1, 2, the Intal Adjustment Factor (IAF) for cells 1 and 2. Then 1, = 1, 2, s the coverage rato for cell, f = 1, 2. Let 2= c 1. The PSF for the combned cell was expressed by Km (2004) as: and For cell 1: for cell 2: (1 + c) f 1 f1(1 + c) f 2, (1). (2) Before collapsng, the PSF for cell 1 s f 1. However, because of collapsng, as shown n equaton (1), f 1 s (1 + c) modfed by, whch s called the Collapsng Adjustment Factor (CAF) for cell 1 by Km, et all f1(1 + c) (2005). Smlarly, for cell 2, the CAF s. Usng the above formulas, we can make the followng f1 observatons: when c = 10 and = 4.0, cell 1 wll lose 73 percent of ts own weght to cell 2. For the same c, f f1 =.25, cell 1 wll gan an addtonal 214 percent of ts own weght from cell 2. ote that ths weght shft s artfcal. Thus, Km (2004) and Km and Tompkns (2007) clamed that the current approach of cell collapsng can ntroduce bas, whch can often be large. Most surveys collapse a cell (row or column) wth another f the PSF (rato) for the cell s greater than 2. Ths standard collapsng procedure allows the PSF of the poorly covered cell to decrease below 2. Hence, Km (2004) proposed to truncate (censor) the PSF for the cell at 2 to make sure that the PSF for that cell s 2 or at least 2, dependng on the method. Km, et al (2007) mplemented these two approaches of weght truncaton n ther smulaton studes and found that the latter 3024
2 Secton on Survey Research Methods outperforms the former and the standard collapsng procedure. When creatng sample weghts, most U.S. government agences combne small race groups such as the Amercan Indans and Asans wth Whtes dsregardng the dfferent coverage ratos of the groups. Ths paper examnes ths methodology usng the 2003 atonal Intervew Survey (HIS) data of the atonal Center for Statstcs (CHS) and reports the effect on the sample weghts and estmates, specfcally for Whtes, Amercan Indans (AI) and Asans. Two alternatve weghtng approaches wll be used n an effort to reduce the bas. 2. Cell Collapsng and Alternatve Weghtng Approaches The HIS uses the followng weghtng matrx: Table 1. Weghtng Matrx < 1 yr Hspanc on-hspanc Black on-hspanc Other M F M F M F In the above table, M stands for male and F for female. The non-hspanc other category, as mentoned before, ncludes all non-hspanc races other than non-hspanc Blacks, (.e., t ncludes Whtes, Amercan Indans, Asans, atve Hawaan and Pacfc Islanders and all multple race groups). It s nterestng to see how much the coverage ratos dffer among the race groups n the others race category. Tables 2a and 2b present coverage ratos for Whtes, Amercan Indans (AI) and Asans by age categores from the 2003 HIS. Table 2a. Ratos for 2003 HIS - Males Age Group Whte AI Asan < Table 2b. Ratos for 2003 HIS - Females Age Group Whte AI Asan < In Table 2a, except for one age group (5 9 years), Whte males always have hgher coverage ratos than Amercan Indan males. Also, Whte males always have hgher coverage ratos than Asan males, wthout excepton. One extreme case s age group less than 1, where the coverage rato for Whte males s.85, whle that for Amercan Indans s.17. The coverage rato for Amercan Indan males age < 1 s only 1/5 of that for Whtes. For the same age group, the Asan coverage rate s less than half that of Whtes. Of 15 male age groups, 7 age groups have coverage ratos less than.5 for Amercan Indans. For the 18 19, and years age groups, coverage ratos for Whtes are also low, but those for Amercan Indans and Asans are even lower, sometmes less than half of that for Whtes. As for females n Table 2b, Whtes always have hgher coverage ratos than Amercan Indans, wth one excepton (10 14 years of age). Also, Whtes are better covered than Asans for all age groups. For the years age group, Whtes have a coverage rate whch s more than 7 tmes better than that of Amercan Indans. For the year age group, the coverage rato for Whtes s more than 6 tmes that of Amercan Indans. Qute often the Whte coverage rate s much better than that of Amercan Indans. 3025
3 Secton on Survey Research Methods The followng example demonstrates the effect on weghts and estmates when two cells wth very dfferent coverage ratos are combned. Example 1. Suppose we have the followng ntally weghted sample counts, control counts and the ntal adjustment factors for 2 cells, one for Whtes and the other for Amercan Indans n Table 3. Table 3. Sample Weghtng Data ˆ AI Whte 17,000 20, When Whte and Amercan Indan cells n the above table are combned, the new PSF for the combned cell s ,000 = , 000 The orgnal PSF for Amercan Indans was 6, but the new PSF s Hence, the new weghted total for Amercan Indans s Snce the control count s 300, we observe an underestmaton of 240, whch equates to an 80 percent underestmaton of Amercan Indans n ths cell. On the other hand, the orgnal PSF for Whtes s 1.18, but the new PSF s Thus, the new weghted total s 20,240, whch s greater than the control count (20,000). In other words, Whtes pcked up an addtonal weght of 240 due to collapsng. Ths amount s 1.2 percent of the control count (20,000). ote that a 1.2 percent overestmaton for Whtes s neglgble, but an 80 percent underestmaton for Amercan Indan s large. In fact, the Collapsng Adjustment Factors (CAFs) for cells 1 and 2 from equatons (1) and (2) have been mplctly appled to f 1 (6) to reach n equaton (3). That s, the CAF for cell 1 s: (20, 000 / ) = (20, 000 / 300) The new PSF for cell 1 s 6( ) = f (3) (4) There s a slght dfference between the values n equatons (3) and (4), whch s due to roundng error. As mentoned before, the category of Whte males age <1 has a much hgher coverage rato than Amercan Indans and Asans. The same observaton can be made for females. Consequently, both Whte males and females age <1 were overestmated by 7 percent n For both genders, n all except two age groups, Whtes are better covered than Amercan Indans, whch causes the former to absorb weghts from the latter. As a result, Amercan Indans, overall, were underestmated by 29.7 percent, as wll be seen n secton 3. Smlarly, Asans were underestmated by 20.7 percent. To rectfy ths problem, we propose two alternatve weghtng procedures. The frst s to weght Amercan Indans and Asans ndependently. Amercan Indans had 197 raw sample cases, whch s enough for ndependent sample weghtng. The number of sample persons s 1,200 for Asans, whch ˆ s more than enough for ndependent sample weghtng. The second procedure s to artfcally nflate to.5 the coverage ratos whch are orgnally lower than.5. Ths s to protect the sample cases n the cells whose coverage ratos are too low, or whose PSF s too hgh. Ths approach s to ensure that the fnal weghted total n the cell s at least half the control count. Accordng to ths approach, the PSF can sometmes go much hgher than 2. Ths approach s somewhat consstent wth the weght truncaton approach by Km, et al (2007). They consdered two approaches of weght truncaton: one allows PSF to go over the threshold (2), but the other does not. The approach proposed here s smlar n sprt to the former. The protecton of the weghts n the poorly covered cells s greater n the approach proposed here because the PSF for ths new approach can ncrease much more than that consdered by Km, et al. Example 2 (Table 4) numercally llustrates the approach proposed here. Table 4. Sample Weghtng Data ˆ AI Whte 17,000 20, In Table 4, we set f for Amercan Indan equal to 2, nstead of 6 as n Table 3. To do so, we had to multply ˆ (50) by 3 to make t 150. In other words, to make sure that f = 2, we had to artfcally nflate ˆ by a factor of 3. If the orgnal f were 3 (ths means ˆ = 100), then we had to artfcally nflate ˆ by a factor of 1.5, nstead of 3. f 3026
4 Secton on Survey Research Methods When Whte and Amercan Indan cells n the above table are combned, the new PSF for the combned cell s ,000 = , 000 The new PSF for Whtes s , but that for Amercan Indans s 3( ) = Compare to for the Amercan Indan cell s PSF. The new cell estmate for Amercan Indans s 50( ) = Snce the control count s 300, we observe an underestmaton of 122, whch equates to an approxmate 41 percent underestmaton of Amercan Indans n ths cell. Ths s a bg mprovement n comparson to the result of the orgnal cell collapsng approach. 3. Alternatve Sample Weghtng When ndependently weghtng the sample for Amercan Indans and Asans, a mnmum raw sample count of 20 was used for cell collapsng. That s, startng wth the age group <1 cell, f a raw sample count was less than 20 for a cell, t was combned wth the next nearest cell. It should be noted that no artfcal nflaton of the weghts was done whle combnng cells n each of the race groups. Artfcally nflatng the weghts was, however, employed n collapsng Amercan Indans and Asans wth Whtes. After weghtng was completed, weghts for each sample unt were accumulated for Amercan Indans and Asans, where the results are shown n Tables 5 and 6, respectvely. Table 5. Amercan Indan Weghtng (n 1,000 s) (5) Total Weght Control Count Current 1,496 (-29.7%) 2,127 Inflated 1,752 (-17.4%) 2,127 Independent 2,127 2,127 As the Table 5 shows, when we rely on the current weghtng procedure,.e., when Amercan Indans are collapsed wth Whtes for weghtng, the weght total for Amercan Indans s 29.7 percent lower than ts control count. On the other hand, when a specal measure was taken to protect the weghts n the cells whose coverage ratos were lower than.5, the weght total mproved over the current approach by 12.3 percent. However, the nflaton approach stll underestmates the control count by 17.4 percent. There are two reasons for ths. Frst, we dd not take any measure to protect the cells whose coverage ratos were hgher than.5, even f coverage rato for Amercan Indans was lower than that for Whtes. Second, even f we gave hgher PSF s to cells whose coverage ratos were lower than.5, we dd not rase the rato all the way to the same level as that for Whtes. As can be predcted, when the ndependent weghtng approach was used, the total weght s the same as control. Table 6. Asan Sample Weghtng (n 1,000 s) Total Weght Control Current 9,369 (-20.7%) 11,817 Inflated 9,753 (-17.5%) 11,817 Independent 11,817 11,817 As shown n Table 6, when Asan cells are collapsed wth Whtes for weghtng, as n the current approach, Asans are underestmated by 20.7 percent. ote that ths underestmaton rate s better than that for Amercan Indans. Ths s because Asans, n general, have better coverage ratos than Amercan Indans for both genders. When the nflaton approach was used, the weghted total mproved over the current approach by only 3.2 percent. Ths mprovement s much lower than that observed for Amercan Indans. The dfference s due to the fact that 16 out of 30 Amercan Indan age groups have coverage ratos less than.5, but for Asans, the same observaton could be made for only 7 age groups. Prevalence rates were calculated for 4 health characterstcs based on the three cell collapsng approaches: dabetes, health nsurance coverage, overnght hosptal stay and asthma. It should be noted that one rate for each race was computed just as n publshed survey reports. Table 7 presents prevalence rates for Amercan Indans. Table 7. Prevalence Rates for Amercan Indans Weghted Total as Denomnator Dabetes Insurance Overnght Hosptal Stay Asthma In Table 7, for all 4 health characterstcs, the prevalence rate for the ndependent weghtng approach s hgher than that for the current weghtng approach. The bggest dfference can be observed for dabetes. The ndependent weghtng approach provdes the prevalence rate for dabetes more than 1 percentage (n absolute term) hgher than the current approach. It s 11 percent hgher n relatve term. The nflaton approach s rate s hgher for 2 characterstcs than the current approach s rate, but 3027
5 Secton on Survey Research Methods t s lower than the ndependent approach s rate. However, for 2 other characterstcs, the prevalence rate for the truncaton approach s lower than that of the current approach. Table 8 presents prevalence rates for Asans. Table 8. Prevalence Rates for Asans Weghted Total as Denomnator Dabetes Insurance Overnght Hosptal Stay Asthma As shown n Table 8, the prevalence rate for the ndependent weghtng approach s hgher than that for the current weghtng approach except for asthma. The truncaton approach provdes prevalence rates closer to that of the ndependent weghtng approach for all varables, except for health nsurance. The dfference for the prevalence rates between the current and the ndependent weghtng approach for Asans s much smaller than that for Amercan Indans. Ths may be due to the fact that the coverage ratos for Asans are much more stable than those for Amercan Indans. ote that n calculatng the prevalence rates n Tables 7 and 8, estmated counts were used for both numerators and denomnators. However, control (populaton) counts nstead of estmated counts (weghted totals) can be used for the denomnator, whle estmated counts are stll used for numerator. For example, suppose researchers want to calculate the prevalence rates for Amercan Indans or Asans resdng n certan age groups regons of the naton, snce CHS report does not show the rates for regons. To do so, they can cumulate weghts of, for example, dabetc people n the regons and compute the prevalence rates usng the cumulated weghts as the numerator and the populaton count as the denomnator. The followng two tables show the prevalence rates calculated n that manner: Table 9. Prevalence Rates for Amercan Indans Control Count as Denomnator Dabetes Insurance Overnght Hosptal Stay Asthma Tables 7 and 9 show the prevalence rates for Amercan Indans. The rates n Table 7 are computed wth the weghted total n the denomnator and those n Table 9, wth the populaton count n the denomnator. The rates n Table 9 are much lower than those n Table 7, except for those for the ndependent weghtng method, whch are the same. The rate for the current approach n Table 9 s 29.7 percent lower than that n Table 7 for each of the four health characterstcs. Smlarly, the rates for the nflaton approach n Table 9 are 17.6 percent lower than those n Table 7. In Table 9, the rates for the current approach are almost one thrd lower than those for the ndependent weghtng approach. The rates for the nflaton approach are between the two approaches. Table 10. Prevalence Rates for Asans Control Count as Denomnator Dabetes Insurance Overnght Hosptal Stay Asthma Both Tables 8 and 10 show the prevalence rates for Asans. The relatonshp between Tables 8 and 10 s the same as that between Table 7 and Table 9. The rates n Table 10 are much lower than the rates n Table 8, except for those for the ndependent weghtng method, whch remans the same. The rate for the current approach n Table 10 s 20.7 percent lower than that n Table 8 for each of the four health characterstcs. Smlarly, the rates for the nflaton approach n Table 10 are 17.4 percent lower than those n Table 8. Agan, these dfferences are due to the dfferent denomnators, that s, the weghted total or the control count. Comparsons between the rates n Table 7 and the rates n Table 9 and between the rates n Table 8 and the rates n Table 10 show that when the prevalence rates are calculated t s better to use the weghted totals as the denomnator for Amercan Indans and Asans. 4. Concludng Remarks Thus far, we have observed that combnng cells wth varyng coverage ratos results n under- and overestmaton of populaton (control) counts. In order to 3028
6 Secton on Survey Research Methods allevate ths problem, we proposed ndependent weghtng and weght nflaton approaches for collapsng cells, mplemented these approaches usng HIS data and compared them wth the current weghtng procedure. Currently, Amercan Indans and Asans are combned wth Whtes for sample weghtng. However, coverage rates for Whtes are better, often much better, than those for Amercan Indans n 28 out of 30 age groups. rates for 3 age groups for Amercan Indans are extremely low,.e., they are n the percent range, whle they are at least 72 percent for Whtes. Because of ths, the current weghtng approach underestmated Amercan Indan by 29.7 percent. Also Whtes consstently had better coverage ratos than Asans, and as a result, the current weghtng approach underestmated Asans by 20.7 percent. We also estmated the prevalence rates for dabetes, health nsurance coverage, overnght hosptal stay and asthma usng the weghts developed by three dfferent ndependent weghtng approach, except for health nsurance. The prevalence rate can be calculated usng two methods. One s to use weghted counts for both numerator and denomnator, and the other s to use weghted counts for the numerator, but populaton counts for the denomnator. The frst approach was used for the tables above. However, f the second approach were to be used, the rates would be underestmated by 29.7 percent for Amercan Indans and by 20.7 percent for Asans wth the current collapsng approach and 17.7 percent and 17.4 percent, respectvely, wth the nflaton approach. Ths s because ther weghted totals are lower than ther respectve populaton counts. Thus, the frst approach s recommended for computng the prevalence rates. The publc use mcro data (PUM) fle from the survey data we used for ths study has been released to the general publc. ote that the PUM fle contans sample weghts for sample persons n the fle. Some data users of the PUM fle mght want to accumulate weghts for Amercan Indans or Asans, say wth dabetes, to come up wth the number of dabetc Amercan Indans or Asans n the naton or some regon of the naton. However, the result would be a gross underestmaton of the true values for the reason mentoned above. A better approach of gettng the number of dabetc Amercan Indans or Asans n the naton or a regon would be to calculate the prevalence rate usng weghted counts for both the numerator and the denomnator and to then multply the rate by the Amercan Indan or Asan populaton count, respectvely. cell collapsng approaches. For all 4 health characterstcs, Amercan Indans show hgher prevalence rates when they are weghted ndependently than when they are weghted as a part of the Other race category (.e., when they are weghted whle combned wth Whtes). The Amercan Indan dabetes prevalence rate s more than 1 percent hgher when the ndependent weghtng approach s used (10.28 %) than when current weghtng approach s used (9.22 %). The weght nflaton approach shows mxed results for Amercan Indans. For 2 characterstcs, the weght nflaton approach showed hgher prevalence rates than the current weghtng approach, whereas for 2 others, the reverse was observed. For Asans, the prevalence rate for the ndependent weghtng approach s hgher than that for the current weghtng approach, except for asthma. The nflaton approach provdes prevalence rates closer to that of the addton, the current approach appears to underperform when compared to the nflaton approach, even though the latter can be further fne tuned. 5. References Km, J. J. (2004). Effect of collapsng rows/columns of weghtng matrx on weghts. Proceedngs of the Secton on Survey Methods Research, Amercan Statstcal Assocaton CD. Km, J.J., L, J., and Vallant, R. (2007). Cell collapsng n poststratfcaton, to be publshed n Survey Methodology. Km, J.J. and Tompkns, L. (2007). Comparsons of current and alternatve collapsng approaches for mproved health estmates. Paper presented at the 11th Bennal CDC/ASTDR Symposum on Statstcal Methods, n Atlanta, Georga, Aprl 17-18, DISCLAIMER: The fndngs and conclusons n ths paper are those of the authors and do not necessarly represent the vews of the atonal Center for Statstcs, Centers for Dsease Control and Preventon. In concluson, the ndependent weghtng approach for Amercan Indans and Asans may produce more realstc weghts, and therefore, more accurate estmates. In 3029
The Integration of the Israel Labour Force Survey with the National Insurance File
The Integraton of the Israel Labour Force Survey wth the Natonal Insurance Fle Natale SHLOMO Central Bureau of Statstcs Kanfey Nesharm St. 66, corner of Bach Street, Jerusalem Natales@cbs.gov.l Abstact:
More informationMeasures of Spread IQR and Deviation. For exam X, calculate the mean, median and mode. For exam Y, calculate the mean, median and mode.
Part 4 Measures of Spread IQR and Devaton In Part we learned how the three measures of center offer dfferent ways of provdng us wth a sngle representatve value for a data set. However, consder the followng
More informationLinear Combinations of Random Variables and Sampling (100 points)
Economcs 30330: Statstcs for Economcs Problem Set 6 Unversty of Notre Dame Instructor: Julo Garín Sprng 2012 Lnear Combnatons of Random Varables and Samplng 100 ponts 1. Four-part problem. Go get some
More informationTests for Two Correlations
PASS Sample Sze Software Chapter 805 Tests for Two Correlatons Introducton The correlaton coeffcent (or correlaton), ρ, s a popular parameter for descrbng the strength of the assocaton between two varables.
More information3: Central Limit Theorem, Systematic Errors
3: Central Lmt Theorem, Systematc Errors 1 Errors 1.1 Central Lmt Theorem Ths theorem s of prme mportance when measurng physcal quanttes because usually the mperfectons n the measurements are due to several
More informationSpurious Seasonal Patterns and Excess Smoothness in the BLS Local Area Unemployment Statistics
Spurous Seasonal Patterns and Excess Smoothness n the BLS Local Area Unemployment Statstcs Keth R. Phllps and Janguo Wang Federal Reserve Bank of Dallas Research Department Workng Paper 1305 September
More informationOCR Statistics 1 Working with data. Section 2: Measures of location
OCR Statstcs 1 Workng wth data Secton 2: Measures of locaton Notes and Examples These notes have sub-sectons on: The medan Estmatng the medan from grouped data The mean Estmatng the mean from grouped data
More informationEvaluating Performance
5 Chapter Evaluatng Performance In Ths Chapter Dollar-Weghted Rate of Return Tme-Weghted Rate of Return Income Rate of Return Prncpal Rate of Return Daly Returns MPT Statstcs 5- Measurng Rates of Return
More informationMgtOp 215 Chapter 13 Dr. Ahn
MgtOp 5 Chapter 3 Dr Ahn Consder two random varables X and Y wth,,, In order to study the relatonshp between the two random varables, we need a numercal measure that descrbes the relatonshp The covarance
More informationIntroduction. Why One-Pass Statistics?
BERKELE RESEARCH GROUP Ths manuscrpt s program documentaton for three ways to calculate the mean, varance, skewness, kurtoss, covarance, correlaton, regresson parameters and other regresson statstcs. Although
More informationCopyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Dr. Wayne A. Taylor
Taylor Enterprses, Inc. ormalzed Indvduals (I ) Chart Copyrght 07 by Taylor Enterprses, Inc., All Rghts Reserved. ormalzed Indvduals (I) Control Chart Dr. Wayne A. Taylor Abstract: The only commonly used
More informationII. Random Variables. Variable Types. Variables Map Outcomes to Numbers
II. Random Varables Random varables operate n much the same way as the outcomes or events n some arbtrary sample space the dstncton s that random varables are smply outcomes that are represented numercally.
More informationFORD MOTOR CREDIT COMPANY SUGGESTED ANSWERS. Richard M. Levich. New York University Stern School of Business. Revised, February 1999
FORD MOTOR CREDIT COMPANY SUGGESTED ANSWERS by Rchard M. Levch New York Unversty Stern School of Busness Revsed, February 1999 1 SETTING UP THE PROBLEM The bond s beng sold to Swss nvestors for a prce
More informationCHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS
CHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS QUESTIONS 9.1. (a) In a log-log model the dependent and all explanatory varables are n the logarthmc form. (b) In the log-ln model the dependent varable
More informationECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE)
ECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE) May 17, 2016 15:30 Frst famly name: Name: DNI/ID: Moble: Second famly Name: GECO/GADE: Instructor: E-mal: Queston 1 A B C Blank Queston 2 A B C Blank Queston
More information3/3/2014. CDS M Phil Econometrics. Vijayamohanan Pillai N. Truncated standard normal distribution for a = 0.5, 0, and 0.5. CDS Mphil Econometrics
Lmted Dependent Varable Models: Tobt an Plla N 1 CDS Mphl Econometrcs Introducton Lmted Dependent Varable Models: Truncaton and Censorng Maddala, G. 1983. Lmted Dependent and Qualtatve Varables n Econometrcs.
More informationAnalysis of Variance and Design of Experiments-II
Analyss of Varance and Desgn of Experments-II MODULE VI LECTURE - 4 SPLIT-PLOT AND STRIP-PLOT DESIGNS Dr. Shalabh Department of Mathematcs & Statstcs Indan Insttute of Technology Kanpur An example to motvate
More informationSpatial Variations in Covariates on Marriage and Marital Fertility: Geographically Weighted Regression Analyses in Japan
Spatal Varatons n Covarates on Marrage and Martal Fertlty: Geographcally Weghted Regresson Analyses n Japan Kenj Kamata (Natonal Insttute of Populaton and Socal Securty Research) Abstract (134) To understand
More informationPrice and Quantity Competition Revisited. Abstract
rce and uantty Competton Revsted X. Henry Wang Unversty of Mssour - Columba Abstract By enlargng the parameter space orgnally consdered by Sngh and Vves (984 to allow for a wder range of cost asymmetry,
More informationInternational ejournals
Avalable onlne at www.nternatonalejournals.com ISSN 0976 1411 Internatonal ejournals Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 MODELING AND PREDICTING URBAN MALE POPULATION OF BANGLADESH:
More informationMode is the value which occurs most frequency. The mode may not exist, and even if it does, it may not be unique.
1.7.4 Mode Mode s the value whch occurs most frequency. The mode may not exst, and even f t does, t may not be unque. For ungrouped data, we smply count the largest frequency of the gven value. If all
More informationElton, Gruber, Brown and Goetzmann. Modern Portfolio Theory and Investment Analysis, 7th Edition. Solutions to Text Problems: Chapter 4
Elton, Gruber, Brown and Goetzmann Modern ortfolo Theory and Investment Analyss, 7th Edton Solutons to Text roblems: Chapter 4 Chapter 4: roblem 1 A. Expected return s the sum of each outcome tmes ts assocated
More informationFinancial mathematics
Fnancal mathematcs Jean-Luc Bouchot jean-luc.bouchot@drexel.edu February 19, 2013 Warnng Ths s a work n progress. I can not ensure t to be mstake free at the moment. It s also lackng some nformaton. But
More informationLikelihood Fits. Craig Blocker Brandeis August 23, 2004
Lkelhood Fts Crag Blocker Brandes August 23, 2004 Outlne I. What s the queston? II. Lkelhood Bascs III. Mathematcal Propertes IV. Uncertantes on Parameters V. Mscellaneous VI. Goodness of Ft VII. Comparson
More informationConsumption Based Asset Pricing
Consumpton Based Asset Prcng Mchael Bar Aprl 25, 208 Contents Introducton 2 Model 2. Prcng rsk-free asset............................... 3 2.2 Prcng rsky assets................................ 4 2.3 Bubbles......................................
More informationFinance 402: Problem Set 1 Solutions
Fnance 402: Problem Set 1 Solutons Note: Where approprate, the fnal answer for each problem s gven n bold talcs for those not nterested n the dscusson of the soluton. 1. The annual coupon rate s 6%. A
More informationWelfare Aspects in the Realignment of Commercial Framework. between Japan and China
Prepared for the 13 th INFORUM World Conference n Huangshan, Chna, July 3 9, 2005 Welfare Aspects n the Realgnment of Commercal Framework between Japan and Chna Toshak Hasegawa Chuo Unversty, Japan Introducton
More informationA Simulation Study to Compare Weighting Methods for Nonresponses in the National Survey of Recent College Graduates
A Smulaton Study to Compare Weghtng Methods for Nonresponses n the Natonal Survey of Recent College Graduates Amang Sukash, Donsg Jang, Sonya Vartvaran, Stephen Cohen 2, Fan Zhang 2 Mathematca Polcy Research.
More informationCapability Analysis. Chapter 255. Introduction. Capability Analysis
Chapter 55 Introducton Ths procedure summarzes the performance of a process based on user-specfed specfcaton lmts. The observed performance as well as the performance relatve to the Normal dstrbuton are
More informationA MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME
A MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME Vesna Radonć Đogatovć, Valentna Radočć Unversty of Belgrade Faculty of Transport and Traffc Engneerng Belgrade, Serba
More informationTests for Two Ordered Categorical Variables
Chapter 253 Tests for Two Ordered Categorcal Varables Introducton Ths module computes power and sample sze for tests of ordered categorcal data such as Lkert scale data. Assumng proportonal odds, such
More informationElements of Economic Analysis II Lecture VI: Industry Supply
Elements of Economc Analyss II Lecture VI: Industry Supply Ka Hao Yang 10/12/2017 In the prevous lecture, we analyzed the frm s supply decson usng a set of smple graphcal analyses. In fact, the dscusson
More information/ Computational Genomics. Normalization
0-80 /02-70 Computatonal Genomcs Normalzaton Gene Expresson Analyss Model Computatonal nformaton fuson Bologcal regulatory networks Pattern Recognton Data Analyss clusterng, classfcaton normalzaton, mss.
More informationChapter 3 Student Lecture Notes 3-1
Chapter 3 Student Lecture otes 3-1 Busness Statstcs: A Decson-Makng Approach 6 th Edton Chapter 3 Descrbng Data Usng umercal Measures 005 Prentce-Hall, Inc. Chap 3-1 Chapter Goals After completng ths chapter,
More informationChapter 3 Descriptive Statistics: Numerical Measures Part B
Sldes Prepared by JOHN S. LOUCKS St. Edward s Unversty Slde 1 Chapter 3 Descrptve Statstcs: Numercal Measures Part B Measures of Dstrbuton Shape, Relatve Locaton, and Detectng Outlers Eploratory Data Analyss
More informationPrivatization and government preference in an international Cournot triopoly
Fernanda A Ferrera Flávo Ferrera Prvatzaton and government preference n an nternatonal Cournot tropoly FERNANDA A FERREIRA and FLÁVIO FERREIRA Appled Management Research Unt (UNIAG School of Hosptalty
More informationSurvey of Math: Chapter 22: Consumer Finance Borrowing Page 1
Survey of Math: Chapter 22: Consumer Fnance Borrowng Page 1 APR and EAR Borrowng s savng looked at from a dfferent perspectve. The dea of smple nterest and compound nterest stll apply. A new term s the
More informationWhich of the following provides the most reasonable approximation to the least squares regression line? (a) y=50+10x (b) Y=50+x (d) Y=1+50x
Whch of the followng provdes the most reasonable approxmaton to the least squares regresson lne? (a) y=50+10x (b) Y=50+x (c) Y=10+50x (d) Y=1+50x (e) Y=10+x In smple lnear regresson the model that s begn
More informationMonetary Tightening Cycles and the Predictability of Economic Activity. by Tobias Adrian and Arturo Estrella * October 2006.
Monetary Tghtenng Cycles and the Predctablty of Economc Actvty by Tobas Adran and Arturo Estrella * October 2006 Abstract Ten out of thrteen monetary tghtenng cycles snce 1955 were followed by ncreases
More informationCS 286r: Matching and Market Design Lecture 2 Combinatorial Markets, Walrasian Equilibrium, Tâtonnement
CS 286r: Matchng and Market Desgn Lecture 2 Combnatoral Markets, Walrasan Equlbrum, Tâtonnement Matchng and Money Recall: Last tme we descrbed the Hungaran Method for computng a maxmumweght bpartte matchng.
More informationAvailable online at ScienceDirect. Procedia Computer Science 24 (2013 ) 9 14
Avalable onlne at www.scencedrect.com ScenceDrect Proceda Computer Scence 24 (2013 ) 9 14 17th Asa Pacfc Symposum on Intellgent and Evolutonary Systems, IES2013 A Proposal of Real-Tme Schedulng Algorthm
More informationSurvey of Math Test #3 Practice Questions Page 1 of 5
Test #3 Practce Questons Page 1 of 5 You wll be able to use a calculator, and wll have to use one to answer some questons. Informaton Provded on Test: Smple Interest: Compound Interest: Deprecaton: A =
More informationUniversity of Toronto November 9, 2006 ECO 209Y MACROECONOMIC THEORY. Term Test #1 L0101 L0201 L0401 L5101 MW MW 1-2 MW 2-3 W 6-8
Department of Economcs Prof. Gustavo Indart Unversty of Toronto November 9, 2006 SOLUTION ECO 209Y MACROECONOMIC THEORY Term Test #1 A LAST NAME FIRST NAME STUDENT NUMBER Crcle your secton of the course:
More informationUniversity of Toronto November 9, 2006 ECO 209Y MACROECONOMIC THEORY. Term Test #1 L0101 L0201 L0401 L5101 MW MW 1-2 MW 2-3 W 6-8
Department of Economcs Prof. Gustavo Indart Unversty of Toronto November 9, 2006 SOLUTION ECO 209Y MACROECONOMIC THEORY Term Test #1 C LAST NAME FIRST NAME STUDENT NUMBER Crcle your secton of the course:
More informationFinite Math - Fall Section Future Value of an Annuity; Sinking Funds
Fnte Math - Fall 2016 Lecture Notes - 9/19/2016 Secton 3.3 - Future Value of an Annuty; Snkng Funds Snkng Funds. We can turn the annutes pcture around and ask how much we would need to depost nto an account
More informationRandom Variables. 8.1 What is a Random Variable? Announcements: Chapter 8
Announcements: Quz starts after class today, ends Monday Last chance to take probablty survey ends Sunday mornng. Next few lectures: Today, Sectons 8.1 to 8. Monday, Secton 7.7 and extra materal Wed, Secton
More informationSolutions to Odd-Numbered End-of-Chapter Exercises: Chapter 12
Introducton to Econometrcs (3 rd Updated Edton) by James H. Stock and Mark W. Watson Solutons to Odd-Numbered End-of-Chapter Exercses: Chapter 1 (Ths verson July 0, 014) Stock/Watson - Introducton to Econometrcs
More informationarxiv: v1 [q-fin.pm] 13 Feb 2018
WHAT IS THE SHARPE RATIO, AND HOW CAN EVERYONE GET IT WRONG? arxv:1802.04413v1 [q-fn.pm] 13 Feb 2018 IGOR RIVIN Abstract. The Sharpe rato s the most wdely used rsk metrc n the quanttatve fnance communty
More informationEDC Introduction
.0 Introducton EDC3 In the last set of notes (EDC), we saw how to use penalty factors n solvng the EDC problem wth losses. In ths set of notes, we want to address two closely related ssues. What are, exactly,
More informationAlternatives to Shewhart Charts
Alternatves to Shewhart Charts CUSUM & EWMA S Wongsa Overvew Revstng Shewhart Control Charts Cumulatve Sum (CUSUM) Control Chart Eponentally Weghted Movng Average (EWMA) Control Chart 2 Revstng Shewhart
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSIO THEORY II Smple Regresson Theory II 00 Samuel L. Baker Assessng how good the regresson equaton s lkely to be Assgnment A gets nto drawng nferences about how close the regresson lne mght
More informationOPERATIONS RESEARCH. Game Theory
OPERATIONS RESEARCH Chapter 2 Game Theory Prof. Bbhas C. Gr Department of Mathematcs Jadavpur Unversty Kolkata, Inda Emal: bcgr.umath@gmal.com 1.0 Introducton Game theory was developed for decson makng
More informationEconomic Design of Short-Run CSP-1 Plan Under Linear Inspection Cost
Tamkang Journal of Scence and Engneerng, Vol. 9, No 1, pp. 19 23 (2006) 19 Economc Desgn of Short-Run CSP-1 Plan Under Lnear Inspecton Cost Chung-Ho Chen 1 * and Chao-Yu Chou 2 1 Department of Industral
More informationScribe: Chris Berlind Date: Feb 1, 2010
CS/CNS/EE 253: Advanced Topcs n Machne Learnng Topc: Dealng wth Partal Feedback #2 Lecturer: Danel Golovn Scrbe: Chrs Berlnd Date: Feb 1, 2010 8.1 Revew In the prevous lecture we began lookng at algorthms
More informationRaising Food Prices and Welfare Change: A Simple Calibration. Xiaohua Yu
Rasng Food Prces and Welfare Change: A Smple Calbraton Xaohua Yu Professor of Agrcultural Economcs Courant Research Centre Poverty, Equty and Growth Unversty of Göttngen CRC-PEG, Wlhelm-weber-Str. 2 3773
More information2) In the medium-run/long-run, a decrease in the budget deficit will produce:
4.02 Quz 2 Solutons Fall 2004 Multple-Choce Questons ) Consder the wage-settng and prce-settng equatons we studed n class. Suppose the markup, µ, equals 0.25, and F(u,z) = -u. What s the natural rate of
More informationSkewness and kurtosis unbiased by Gaussian uncertainties
Skewness and kurtoss unbased by Gaussan uncertantes Lorenzo Rmoldn Observatore astronomque de l Unversté de Genève, chemn des Mallettes 5, CH-9 Versox, Swtzerland ISDC Data Centre for Astrophyscs, Unversté
More informationUncertainties in the Swedish PPI and SPPI
European Conference on Qualty n Offcal Statstcs (Q016) Madrd, 31 May-3 June 016 Uncertantes n the Swedsh PPI and SPPI Krstna Strandberg 1, Anders orberg, Marcus Frdén 3 1 Statstcs Sweden, Stockholm, Sweden;
More informationThe Effects of Industrial Structure Change on Economic Growth in China Based on LMDI Decomposition Approach
216 Internatonal Conference on Mathematcal, Computatonal and Statstcal Scences and Engneerng (MCSSE 216) ISBN: 978-1-6595-96- he Effects of Industral Structure Change on Economc Growth n Chna Based on
More informationFinal Exam. 7. (10 points) Please state whether each of the following statements is true or false. No explanation needed.
Fnal Exam Fall 4 Econ 8-67 Closed Book. Formula Sheet Provded. Calculators OK. Tme Allowed: hours Please wrte your answers on the page below each queston. (5 ponts) Assume that the rsk-free nterest rate
More informationWork, Offers, and Take-Up: Decomposing the Source of Recent Declines in Employer- Sponsored Insurance
Work, Offers, and Take-Up: Decomposng the Source of Recent Declnes n Employer- Sponsored Insurance Lnda J. Blumberg and John Holahan The Natonal Bureau of Economc Research (NBER) determned that a recesson
More informationCOS 511: Theoretical Machine Learning. Lecturer: Rob Schapire Lecture #21 Scribe: Lawrence Diao April 23, 2013
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #21 Scrbe: Lawrence Dao Aprl 23, 2013 1 On-Lne Log Loss To recap the end of the last lecture, we have the followng on-lne problem wth N
More informationOn Robust Small Area Estimation Using a Simple. Random Effects Model
On Robust Small Area Estmaton Usng a Smple Random Effects Model N. G. N. PRASAD and J. N. K. RAO 1 ABSTRACT Robust small area estmaton s studed under a smple random effects model consstng of a basc (or
More informationIncorrect Beliefs. Overconfidence. Types of Overconfidence. Outline. Overprecision 4/15/2017. Behavioral Economics Mark Dean Spring 2017
Incorrect Belefs Overconfdence Behavoral Economcs Mark Dean Sprng 2017 In objectve EU we assumed that everyone agreed on what the probabltes of dfferent events were In subjectve expected utlty theory we
More informationParallel Prefix addition
Marcelo Kryger Sudent ID 015629850 Parallel Prefx addton The parallel prefx adder presented next, performs the addton of two bnary numbers n tme of complexty O(log n) and lnear cost O(n). Lets notce the
More informationRisk and Return: The Security Markets Line
FIN 614 Rsk and Return 3: Markets Professor Robert B.H. Hauswald Kogod School of Busness, AU 1/25/2011 Rsk and Return: Markets Robert B.H. Hauswald 1 Rsk and Return: The Securty Markets Lne From securtes
More informationHewlett Packard 10BII Calculator
Hewlett Packard 0BII Calculator Keystrokes for the HP 0BII are shown n the tet. However, takng a mnute to revew the Quk Start secton, below, wll be very helpful n gettng started wth your calculator. Note:
More informationTHIS PAPER SHOULD NOT BE OPENED UNTIL PERMISSION HAS BEEN GIVEN BY THE INVIGILATOR.
UNVERSTY OF SWAZLAND FACULTY OF SOCAL SCENCES DEPARTMENT OF STATSTCS AND DEMOGRAPHY MAN EXAMNATON 2016 TTTLE OF PAPER: DEMOGRAPHC METHODS 1 COURSE NUMBER: DEM 201 TME ALLOWED: 2 Hours NSTRUCTONS: ANSWER
More informationUNIVERSITY OF NOTTINGHAM
UNIVERSITY OF NOTTINGHAM SCHOOL OF ECONOMICS DISCUSSION PAPER 99/28 Welfare Analyss n a Cournot Game wth a Publc Good by Indraneel Dasgupta School of Economcs, Unversty of Nottngham, Nottngham NG7 2RD,
More informationXiaoli Lu VA Cooperative Studies Program, Perry Point, MD
A SAS Program to Construct Smultaneous Confdence Intervals for Relatve Rsk Xaol Lu VA Cooperatve Studes Program, Perry Pont, MD ABSTRACT Assessng adverse effects s crtcal n any clncal tral or nterventonal
More informationDates July 2010, Revised November 2010, Final Revised March Total Words 7,462 (5,962 Words, 5 Tables, 1 Figure) *Corresponding author
Investgatng the Effects of Underreportng of Crash Data on Three Commonly Used Traffc Crash Severty Models: Multnomal Logt, Ordered Probt and Mxed Logt Models Fan Ye* Graduate Research Assstant Zachry Department
More informationMarket Opening and Stock Market Behavior: Taiwan s Experience
Internatonal Journal of Busness and Economcs, 00, Vol., No., 9-5 Maret Openng and Stoc Maret Behavor: Tawan s Experence Q L * Department of Economcs, Texas A&M Unversty, U.S.A. and Department of Economcs,
More informationPhysics 4A. Error Analysis or Experimental Uncertainty. Error
Physcs 4A Error Analyss or Expermental Uncertanty Slde Slde 2 Slde 3 Slde 4 Slde 5 Slde 6 Slde 7 Slde 8 Slde 9 Slde 0 Slde Slde 2 Slde 3 Slde 4 Slde 5 Slde 6 Slde 7 Slde 8 Slde 9 Slde 20 Slde 2 Error n
More informationISE High Income Index Methodology
ISE Hgh Income Index Methodology Index Descrpton The ISE Hgh Income Index s desgned to track the returns and ncome of the top 30 U.S lsted Closed-End Funds. Index Calculaton The ISE Hgh Income Index s
More informationPASS Sample Size Software. :log
PASS Sample Sze Software Chapter 70 Probt Analyss Introducton Probt and lot analyss may be used for comparatve LD 50 studes for testn the effcacy of drus desned to prevent lethalty. Ths proram module presents
More informationISE Cloud Computing Index Methodology
ISE Cloud Computng Index Methodology Index Descrpton The ISE Cloud Computng Index s desgned to track the performance of companes nvolved n the cloud computng ndustry. Index Calculaton The ISE Cloud Computng
More informationTaxation and Externalities. - Much recent discussion of policy towards externalities, e.g., global warming debate/kyoto
Taxaton and Externaltes - Much recent dscusson of polcy towards externaltes, e.g., global warmng debate/kyoto - Increasng share of tax revenue from envronmental taxaton 6 percent n OECD - Envronmental
More informationQuiz 2 Answers PART I
Quz 2 nswers PRT I 1) False, captal ccumulaton alone wll not sustan growth n output per worker n the long run due to dmnshng margnal returns to captal as more and more captal s added to a gven number of
More informationCyclic Scheduling in a Job shop with Multiple Assembly Firms
Proceedngs of the 0 Internatonal Conference on Industral Engneerng and Operatons Management Kuala Lumpur, Malaysa, January 4, 0 Cyclc Schedulng n a Job shop wth Multple Assembly Frms Tetsuya Kana and Koch
More informationarxiv:cond-mat/ v1 [cond-mat.other] 28 Nov 2004
arxv:cond-mat/0411699v1 [cond-mat.other] 28 Nov 2004 Estmatng Probabltes of Default for Low Default Portfolos Katja Pluto and Drk Tasche November 23, 2004 Abstract For credt rsk management purposes n general,
More informationA Bootstrap Confidence Limit for Process Capability Indices
A ootstrap Confdence Lmt for Process Capablty Indces YANG Janfeng School of usness, Zhengzhou Unversty, P.R.Chna, 450001 Abstract The process capablty ndces are wdely used by qualty professonals as an
More informationFall 2017 Social Sciences 7418 University of Wisconsin-Madison Problem Set 3 Answers
ublc Affars 854 enze D. Chnn Fall 07 Socal Scences 748 Unversty of Wsconsn-adson roblem Set 3 Answers Due n Lecture on Wednesday, November st. " Box n" your answers to the algebrac questons.. Fscal polcy
More informationTHE MARKET PORTFOLIO MAY BE MEAN-VARIANCE EFFICIENT AFTER ALL
THE ARKET PORTFOIO AY BE EA-VARIACE EFFICIET AFTER A OSHE EVY and RICHARD RO ABSTRACT Testng the CAP bols down to testng the mean-varance effcency of the market portfolo. any studes have examned the meanvarance
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE SOLUTIONS Interest Theory
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE SOLUTIONS Interest Theory Ths page ndcates changes made to Study Note FM-09-05. January 14, 014: Questons and solutons 58 60 were added.
More informationNonresponse in the Norwegian Labour Force Survey (LFS): using administrative information to describe trends
Notater Documents 54/2012 Ib Thomsen and Ole Vllund Nonresponse n the Norwegan Labour Force Survey (LFS): usng admnstratve nformaton to descrbe trends Documents 54/2012 Ib Thomsen and Ole Vllund Nonresponse
More informationNumerical Analysis ECIV 3306 Chapter 6
The Islamc Unversty o Gaza Faculty o Engneerng Cvl Engneerng Department Numercal Analyss ECIV 3306 Chapter 6 Open Methods & System o Non-lnear Eqs Assocate Pro. Mazen Abualtaye Cvl Engneerng Department,
More informationHarmonised Labour Cost Index. Methodology
Harmonsed Labour Cost Index Methodology March 2013 Index 1 Introducton 3 2 Scope, coverage and reference perod 4 3 Defntons 5 4 Sources of nformaton 7 5 Formulae employed 9 6 Results obtaned 10 7 Seres
More informationASSESSING GOODNESS OF FIT OF GENERALIZED LINEAR MODELS TO SPARSE DATA USING HIGHER ORDER MOMENT CORRECTIONS
ASSESSING GOODNESS OF FIT OF GENERALIZED LINEAR MODELS TO SPARSE DATA USING HIGHER ORDER MOMENT CORRECTIONS S. R. PAUL Department of Mathematcs & Statstcs, Unversty of Wndsor, Wndsor, ON N9B 3P4, Canada
More informationS yi a bx i cx yi a bx i cx 2 i =0. yi a bx i cx 2 i xi =0. yi a bx i cx 2 i x
LEAST-SQUARES FIT (Chapter 8) Ft the best straght lne (parabola, etc.) to a gven set of ponts. Ths wll be done by mnmzng the sum of squares of the vertcal dstances (called resduals) from the ponts to the
More informationFacility Location Problem. Learning objectives. Antti Salonen Farzaneh Ahmadzadeh
Antt Salonen Farzaneh Ahmadzadeh 1 Faclty Locaton Problem The study of faclty locaton problems, also known as locaton analyss, s a branch of operatons research concerned wth the optmal placement of facltes
More informationPivot Points for CQG - Overview
Pvot Ponts for CQG - Overvew By Bran Bell Introducton Pvot ponts are a well-known technque used by floor traders to calculate ntraday support and resstance levels. Ths technque has been around for decades,
More informationISyE 512 Chapter 9. CUSUM and EWMA Control Charts. Instructor: Prof. Kaibo Liu. Department of Industrial and Systems Engineering UW-Madison
ISyE 512 hapter 9 USUM and EWMA ontrol harts Instructor: Prof. Kabo Lu Department of Industral and Systems Engneerng UW-Madson Emal: klu8@wsc.edu Offce: Room 317 (Mechancal Engneerng Buldng) ISyE 512 Instructor:
More informationCreating a zero coupon curve by bootstrapping with cubic splines.
MMA 708 Analytcal Fnance II Creatng a zero coupon curve by bootstrappng wth cubc splnes. erg Gryshkevych Professor: Jan R. M. Röman 0.2.200 Dvson of Appled Mathematcs chool of Educaton, Culture and Communcaton
More informationUNIVERSITY OF VICTORIA Midterm June 6, 2018 Solutions
UIVERSITY OF VICTORIA Mdterm June 6, 08 Solutons Econ 45 Summer A0 08 age AME: STUDET UMBER: V00 Course ame & o. Descrptve Statstcs and robablty Economcs 45 Secton(s) A0 CR: 3067 Instructor: Betty Johnson
More informationExamining the Validity of Credit Ratings Assigned to Credit Derivatives
Examnng the Valdty of redt atngs Assgned to redt Dervatves hh-we Lee Department of Fnance, Natonal Tape ollege of Busness No. 321, Sec. 1, h-nan d., Tape 100, Tawan heng-kun Kuo Department of Internatonal
More informationRandom Variables. b 2.
Random Varables Generally the object of an nvestgators nterest s not necessarly the acton n the sample space but rather some functon of t. Techncally a real valued functon or mappng whose doman s the sample
More informationStochastic Generation of Daily Rainfall Data
Stochastc Generaton of Daly Ranfall Data Srkanthan, R. CRC for Catchment Hydrology, Bureau of Meteorology, Melbourne, Australa, E-Mal: r.srkanthan@bom.gov.au Keywords: Stochastc generaton; daly ranfall;
More informationConstruction Rules for Morningstar Canada Momentum Index SM
Constructon Rules for Mornngstar Canada Momentum Index SM Mornngstar Methodology Paper January 2012 2012 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property of Mornngstar,
More informationDomestic Savings and International Capital Flows
Domestc Savngs and Internatonal Captal Flows Martn Feldsten and Charles Horoka The Economc Journal, June 1980 Presented by Mchael Mbate and Chrstoph Schnke Introducton The 2 Vews of Internatonal Captal
More informationStandardization. Stan Becker, PhD Bloomberg School of Public Health
Ths work s lcensed under a Creatve Commons Attrbuton-NonCommercal-ShareAlke Lcense. Your use of ths materal consttutes acceptance of that lcense and the condtons of use of materals on ths ste. Copyrght
More information