Bagdonavièus / Kruopis / Nikulin Nonparametric Tests for Censored Data

1. Auflage 2013
ISBN: 978-1-118-60213-3
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 234 Seiten, E-Book

This book concerns testing hypotheses in non-parametric models.Generalizations of many non-parametric tests to the case ofcensored and truncated data are considered. Most of the testresults are proved and real applications are illustrated usingexamples. Theories and exercises are provided. The incorrect use ofmany tests applying most statistical software is highlighted anddiscussed.

Autoren/Hrsg.

Bagdonavièus, Vilijandas

Kruopis, Julius

Nikulin, Mikhail

Inhaltsverzeichnis

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 families36
2.4. Chi-squared tests for other families 51
2.5. Exercises 59
2.6. Answers 60
Chapter 3. Homogeneity Tests for IndependentPopulations 63
3.1 Data 64
3.2 Weighted logrank statistics 64
3.3. Logrank test statistics as weighted sums of differencesbetween observed and expected number of failures 66
3.4 Examples of weights 67
3.5. Weighted logrank statistics as modified scorestatistics 69
3.6. The first two moments of weighted logrankstatistics 71
3.7. Asymptotic properties of weighted logrankstatistics 73
3.8. Weighted logrank tests 80
3.9. Homogeneity testing when alternatives are crossings ofsurvival functions 85
3.10. Exercises 98
3.11. Answers 102
Chapter 4. Homogeneity Tests for RelatedPopulations 105
4.1. Paired samples 106
4.2. Logrank-type tests for homogeneity of related k > 2samples 119
4.3. Homogeneity tests for related samples against crossingmarginal 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 Coxmodel 127
5.2. Chi-squared goodness-of-fit tests for parametric AFTmodels 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