This book concerns testing hypotheses in non-parametric models. Generalizations of many non-parametric tests to the case of censored and truncated data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed.
This book concerns testing hypotheses in non-parametric models. Generalizations of many non-parametric tests to the case of censored and truncated data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Vilijandas Bagdonavicius is Professor of Mathematics at the University of Vilnius in Lithuania. His main research areas are statistics, reliability and survival analysis. Julius Kruopis is Associate Professor of Mathematics at the University of Vilnius in Lithuania. His main research areas are statistics and quality control. Mikhail S. Nikulin is a member of the Institute of Mathematics in Bordeaux, France.
Inhaltsangabe
Preface xi Terms and Notation xv Chapter 1. Censored and Truncated Data 1 1.1. Right-censored data 2 1.2. Left truncation 12 1.3. Left truncation and right censoring 14 1.4. Nelson-Aalen and Kaplan-Meier estimators 15 1.5 Bibliographic notes 17 Chapter 2. Chi-squared Tests 19 2.1. Chi-squared test for composite hypothesis 19 2.2. Chi-squared test for exponential distributions 31 2.3. Chi-squared tests for shape-scale distribution families 36 2.4. Chi-squared tests for other families 51 2.5. Exercises 59 2.6. Answers 60 Chapter 3. Homogeneity Tests for Independent Populations 63 3.1 Data 64 3.2 Weighted logrank statistics 64 3.3. Logrank test statistics as weighted sums of differences between observed and expected number of failures 66 3.4 Examples of weights 67 3.5. Weighted logrank statistics as modified score statistics 69 3.6. The first two moments of weighted logrank statistics 71 3.7. Asymptotic properties of weighted logrank statistics 73 3.8. Weighted logrank tests 80 3.9. Homogeneity testing when alternatives are crossings of survival functions 85 3.10. Exercises 98 3.11. Answers 102 Chapter 4. Homogeneity Tests for Related Populations 105 4.1. Paired samples 106 > 2 samples 119 4.3. Homogeneity tests for related samples against crossing marginal survival functions alternatives 122 4.4. Exercises 125 4.5 Answers 126 Chapter 5. Goodness-of-fit for Regression Models 127 5.1. Goodness-of-fit for the semi-parametric Cox model 127 5.2. Chi-squared goodness-of-fit tests for parametric AFT models 142 5.3. Chi-squared test for the exponential AFT model 153 5.4. Chi-squared tests for scale-shape AFT models 159 Bibliographic notes 172 5.6. Exercises 173 Answers 174 APPENDICES 177 Appendix A. 179 Appendix B. 191 Appendix C. 211 Bibliography 225 Index 231
Preface xi Terms and Notation xv Chapter 1. Censored and Truncated Data 1 1.1. Right-censored data 2 1.2. Left truncation 12 1.3. Left truncation and right censoring 14 1.4. Nelson-Aalen and Kaplan-Meier estimators 15 1.5 Bibliographic notes 17 Chapter 2. Chi-squared Tests 19 2.1. Chi-squared test for composite hypothesis 19 2.2. Chi-squared test for exponential distributions 31 2.3. Chi-squared tests for shape-scale distribution families 36 2.4. Chi-squared tests for other families 51 2.5. Exercises 59 2.6. Answers 60 Chapter 3. Homogeneity Tests for Independent Populations 63 3.1 Data 64 3.2 Weighted logrank statistics 64 3.3. Logrank test statistics as weighted sums of differences between observed and expected number of failures 66 3.4 Examples of weights 67 3.5. Weighted logrank statistics as modified score statistics 69 3.6. The first two moments of weighted logrank statistics 71 3.7. Asymptotic properties of weighted logrank statistics 73 3.8. Weighted logrank tests 80 3.9. Homogeneity testing when alternatives are crossings of survival functions 85 3.10. Exercises 98 3.11. Answers 102 Chapter 4. Homogeneity Tests for Related Populations 105 4.1. Paired samples 106 > 2 samples 119 4.3. Homogeneity tests for related samples against crossing marginal survival functions alternatives 122 4.4. Exercises 125 4.5 Answers 126 Chapter 5. Goodness-of-fit for Regression Models 127 5.1. Goodness-of-fit for the semi-parametric Cox model 127 5.2. Chi-squared goodness-of-fit tests for parametric AFT models 142 5.3. Chi-squared test for the exponential AFT model 153 5.4. Chi-squared tests for scale-shape AFT models 159 Bibliographic notes 172 5.6. Exercises 173 Answers 174 APPENDICES 177 Appendix A. 179 Appendix B. 191 Appendix C. 211 Bibliography 225 Index 231
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