Contents. Statistical Science

Transcription

1 Contents Part I Statistical Science The Non-mathematical Side of Statistics... 3 João A. Branco 1 Statistics and Mathematics Statistics Is Not Mathematics The Non-mathematical Side of Statistics The Problem Data in Context Fisher s Chi-Square Analysis A Cute Little Theorem Final Remarks References Outliers: The Strength of Minors Fernando Rosado 1 Statistics as a Science Statistical Science: Inference and Decision The Need of Outliers Fortune/Chance Decide!? Outliers: A Path in Research In Perspective References Resampling Methodologies in the Field of Statistics of Univariate Extremes M. Ivette Gomes 1 Extreme Value Theory: A Brief Introduction EVI-Estimators Under Consideration Resampling Methodologies The Generalised Jackknife Methodology and Bias Reduction The Bootstrap Methodology for the Estimation of Sample Fractions Concluding Remarks References vii

2 viii Contents Robust Functional Principal Component Analysis Juan Lucas Bali and Graciela Boente 1 Introduction Preliminaries and Notation The Problem Robust Proposals for FPCA Lip Data Example Final Comments References Testing the Maximum by the Mean in Quantitative Group Tests João Paulo Martins, Rui Santos, and Ricardo Sousa 1 Introduction Dorfman s Procedures and Its Extensions The Pooled Sample Tests T 1 Methodology: Using the Distribution of the Sample Mean T 2 Methodology: Using a Simulation Method Simulations Results Conclusion References Testing Serial Correlation Using the Gauss Newton Regression Efigénio Rebelo, Patrícia Oom do Valle, and Rui Nunes 1 Introduction The Gauss Newton Regression Testing for Evidence of Serial Correlation Testing for Common Factor Restrictions Test T Test Conclusions References Part II Probability and Stochastic Processes Cantor Sets with Random Repair M. Fátima Brilhante, Dinis Pestana, and M. Luísa Rocha 1 Introduction Stuttering Cantor-Like Random Sets Construction Procedure Random Repair Benefits for Cantor-Like Sets References Nearest Neighbor Connectivity in Two-Dimensional Multihop MANETs Gonçalo Jacinto, Nelson Antunes, and António Pacheco 1 Introduction Model Description... 87

3 Contents ix 3 Hop Count Distribution Numerical Results Conclusion References Modeling Human Population Death Rates: A Bi-Dimensional Stochastic Gompertz Model with Correlated Wiener Processes Sandra Lagarto and Carlos A. Braumann 1 Introduction The Stochastic Mortality Model The Bi-Dimensional Stochastic Gompertz Model with Correlated Wiener Processes Application to Human Portuguese Population Death Rates Testing for Correlations Between Sexes Conclusions/Future Work References Consequences of an Incorrect Model Specification on Population Growth Clara Carlos and Carlos A. Braumann 1 Introduction Model Extinction Times Conclusions References Individual Growth in a Random Environment: An Optimization Problem Patrícia A. Filipe, Carlos A. Braumann, Clara Carlos, and Carlos J. Roquete 1 Introduction SDE Model for Individual Growth Optimization Profit Optimization by Age Profit Optimization by Weight Final Remarks References Valuation of Bond Options Under the CIR Model: Some Computational Remarks Manuela Larguinho, José Carlos Dias, and Carlos A. Braumann 1 Introduction Noncentral 2 Distribution and Alternative Methods The Gamma Series Method The Schroder Method The Ding Method The Benton and Krishnamoorthy Method

4 x Contents 3 Bond Options Under the CIR Model Zero-Coupon and Coupon Bonds Bond Options Numerical Analysis Benchmark Selection Bond Options with Alternative Methods Conclusion References Part III Extremes A Semi-parametric Estimator of a Shape Second-Order Parameter Frederico Caeiro and M. Ivette Gomes 1 Introduction Estimation of the Second-Order Parameter A Review of Some Estimators in the Literature A New Estimator for the Second-Order Parameter Main Asymptotic Results Applications to Simulated and Real Data A Case Study in the Field of Insurance Simulated Data References Peaks Over Random Threshold Asymptotically Best Linear Estimation of the Extreme Value Index Lígia Henriques-Rodrigues and M. Ivette Gomes 1 Introduction and Scope of the Paper PORT EVI-Estimation Second-Order Framework for Heavy-Tailed Models Under a Non-Null Shift Asymptotically Best Linear Unbiased Estimation of the EVI Adaptive PORT-ABL-Hill Estimation An Application to Financial Data Some Final Remarks References Extremal Quantiles, Value-at-Risk, Quasi-PORT and DPOT P. Araújo Santos and M.I. Fraga Alves 1 Introduction VaR Models Quasi-PORT DPOT Other Models Out-of-Sample Study with the DJIA Index References

5 Contents xi The MOP EVI-Estimator Revisited M. Fátima Brilhante, M. Ivette Gomes, and Dinis Pestana 1 Introduction and Preliminaries The Class of MOP EVI-Estimators Finite Sample Properties of the MOP Class of EVI-Estimators A Brief Note on the Asymptotic Comparison of MOP EVI-Estimators at Optimal Levels Simple Adaptive Selections of the Tuning Parameters References Tail Dependence of a Pareto Process Marta Ferreira 1 Introduction Measures of Tail Dependence Tail Dependence of YARP(III)(1) References Application of the Theory of Extremes to the Study of Precipitation in Madeira Island: Statistical Choice of Extreme Domains of Attraction Délia Gouveia, Luiz Guerreiro Lopes, and Sandra Mendonça 1 Introduction Methods and Data Results and Discussion Final Remarks References The Traveling Salesman Problem and the Gnedenko Theorem Tiago Salvador and Manuel Cabral Morais 1 Traveling Salesman Problem: Definition and a Few Milestones Complexity, Approximate Algorithms, and Statistical Approach Statistical Analysis of the Results of the -Optimal and -Optimal Greedy Algorithms; Concluding Remarks References Part IV Statistical Applications Brugada Syndrome Diagnosis: Three Approaches to Combining Diagnostic Markers Carla Henriques, Ana Cristina Matos, and Luís Ferreira dos Santos 1 Introduction ECG Markers to Identify Mutation Carriers Combining the Markers: Multivariate Analysis Discriminant Analysis Distribution-Free Approach Logistic Regression

6 xii Contents 4 Conclusions References Hierarchical Normal Mixture Model to Analyse HIV/AIDS LOS Sara Simões Dias, Valeska Andreozzi, and Maria Oliveira Martins 1 Introduction Hierarchical Finite Mixture Model Application to HIV/AIDS LOS Data Results Discussion Conclusion References Volatility and Returns of the Main Stock Indices Thelma Sáfadi and Airlane P. Alencar 1 Introduction Methods Results Conclusions References Using INLA to Estimate a Highly Dimensional Spatial Model for Forest Fires in Portugal Isabel Natário, M. Manuela Oliveira, and Susete Marques 1 Introduction A Model for Forest Fires Bayesian Estimation Markov Chain Monte Carlo Integrated Nested Laplace Approximation Application: Forest Fires in Mainland Portugal Concluding Remarks References Forecast Intervals with Boot.EXPOS Clara Cordeiro and M. Manuela Neves 1 Introduction Bootstrap and EXPOS Together: Boot.EXPOS, a Team Work Forecast Intervals in EXPOS Forecast Intervals in Boot.EXPOS Case Study Conclusions References

7 Contents xiii Table-Graph: A New Approach to Visualize Multivariate Data. Analysis of Chronic Diseases in Portugal Alexandra Pinto 1 Introduction Objectives, Material and Methods Table-Graph Results and Discussion Conclusion References Application of Item Response Theory to Mathematics High School Exams in Portugal Gonçalo Jacinto, Paulo Infante, and Claudia Pereira 1 Introduction Unidimensional IRT Models for Dichotomous Responses Critical Analysis of the Obtained Results Results for the First and Second Calls of the 2008 Exams Results for the First and Second Calls of the 2010 Exams Some Remarks References Évora Residents and Sports Activity Luísa Carvalho, Paulo Infante, and Anabela Afonso 1 Introduction Methodology Sports Practice Characterization Practitioner Profile Final Remarks References Index

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