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.
Tabella dei contenuti
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
4.2. Logrank-type tests for homogeneity of related k > 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
Circa l’autore
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.
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