Vilijandas Bagdonavicius,
V Bagdonavicius,
Julius Kruopis,
Mikhail S. (Universite Victor Segalen, Bordeaux 2, France) Nikulin
e.a.
John Wiley & Sons
e druk, 2010
9781848212893
Nonparametric Tests for Censored Data
Specificaties
Gebonden, 252 blz.
|
Engels
John Wiley & Sons |
e druk, 2010
ISBN13: 9781848212893
Rubricering
Juridisch
:
Onderdeel van serie
ISTE
Verwachte levertijd ongeveer 9 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9781848212893
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:252
Uitgever:John Wiley & Sons
Serie:ISTE
Inhoudsopgave
<p>Preface xi</p>
<p>Terms and Notation xv</p>
<p>Chapter 1. Censored and Truncated Data 1</p>
<p>1.1. Right–censored data 2</p>
<p>1.2. Left truncation 12</p>
<p>1.3. Left truncation and right censoring 14</p>
<p>1.4. Nelson Aalen and Kaplan Meier estimators 15</p>
<p>1.5 Bibliographic notes 17</p>
<p>Chapter 2. Chi–squared Tests 19</p>
<p>2.1. Chi–squared test for composite hypothesis 19</p>
<p>2.2. Chi–squared test for exponential distributions 31</p>
<p>2.3. Chi–squared tests for shape–scale distribution families 36</p>
<p>2.4. Chi–squared tests for other families 51</p>
<p>2.5. Exercises 59</p>
<p>2.6. Answers 60</p>
<p>Chapter 3. Homogeneity Tests for Independent Populations 63</p>
<p>3.1 Data 64</p>
<p>3.2 Weighted logrank statistics 64</p>
<p>3.3. Logrank test statistics as weighted sums of differences between observed and expected number of failures 66</p>
<p>3.4 Examples of weights 67</p>
<p>3.5. Weighted logrank statistics as modified score statistics 69</p>
<p>3.6. The first two moments of weighted logrank statistics 71</p>
<p>3.7. Asymptotic properties of weighted logrank statistics 73</p>
<p>3.8. Weighted logrank tests 80</p>
<p>3.9. Homogeneity testing when alternatives are crossings of survival functions 85</p>
<p>3.10. Exercises 98</p>
<p>3.11. Answers 102</p>
<p>Chapter 4. Homogeneity Tests for Related Populations 105</p>
<p>4.1. Paired samples 106</p>
<p>4.2. Logrank–type tests for homogeneity of related k > 2 samples 119</p>
<p>4.3. Homogeneity tests for related samples against crossing marginal survival functions alternatives 122</p>
<p>4.4. Exercises 125</p>
<p>4.5 Answers 126</p>
<p>Chapter 5. Goodness–of–fit for Regression Models 127</p>
<p>5.1. Goodness–of–fit for the semi–parametric Cox model 127</p>
<p>5.2. Chi–squared goodness–of–fit tests for parametric AFT models 142</p>
<p>5.3. Chi–squared test for the exponential AFT model 153</p>
<p>5.4. Chi–squared tests for scale–shape AFT models 159</p>
<p>Bibliographic notes 172</p>
<p>5.6. Exercises 173</p>
<p>Answers 174</p>
<p>APPENDICES 177</p>
<p>Appendix A. 179</p>
<p>Appendix B. 191</p>
<p>Appendix C. 211</p>
<p>Bibliography 225</p>
<p>Index 231</p>
<p>Terms and Notation xv</p>
<p>Chapter 1. Censored and Truncated Data 1</p>
<p>1.1. Right–censored data 2</p>
<p>1.2. Left truncation 12</p>
<p>1.3. Left truncation and right censoring 14</p>
<p>1.4. Nelson Aalen and Kaplan Meier estimators 15</p>
<p>1.5 Bibliographic notes 17</p>
<p>Chapter 2. Chi–squared Tests 19</p>
<p>2.1. Chi–squared test for composite hypothesis 19</p>
<p>2.2. Chi–squared test for exponential distributions 31</p>
<p>2.3. Chi–squared tests for shape–scale distribution families 36</p>
<p>2.4. Chi–squared tests for other families 51</p>
<p>2.5. Exercises 59</p>
<p>2.6. Answers 60</p>
<p>Chapter 3. Homogeneity Tests for Independent Populations 63</p>
<p>3.1 Data 64</p>
<p>3.2 Weighted logrank statistics 64</p>
<p>3.3. Logrank test statistics as weighted sums of differences between observed and expected number of failures 66</p>
<p>3.4 Examples of weights 67</p>
<p>3.5. Weighted logrank statistics as modified score statistics 69</p>
<p>3.6. The first two moments of weighted logrank statistics 71</p>
<p>3.7. Asymptotic properties of weighted logrank statistics 73</p>
<p>3.8. Weighted logrank tests 80</p>
<p>3.9. Homogeneity testing when alternatives are crossings of survival functions 85</p>
<p>3.10. Exercises 98</p>
<p>3.11. Answers 102</p>
<p>Chapter 4. Homogeneity Tests for Related Populations 105</p>
<p>4.1. Paired samples 106</p>
<p>4.2. Logrank–type tests for homogeneity of related k > 2 samples 119</p>
<p>4.3. Homogeneity tests for related samples against crossing marginal survival functions alternatives 122</p>
<p>4.4. Exercises 125</p>
<p>4.5 Answers 126</p>
<p>Chapter 5. Goodness–of–fit for Regression Models 127</p>
<p>5.1. Goodness–of–fit for the semi–parametric Cox model 127</p>
<p>5.2. Chi–squared goodness–of–fit tests for parametric AFT models 142</p>
<p>5.3. Chi–squared test for the exponential AFT model 153</p>
<p>5.4. Chi–squared tests for scale–shape AFT models 159</p>
<p>Bibliographic notes 172</p>
<p>5.6. Exercises 173</p>
<p>Answers 174</p>
<p>APPENDICES 177</p>
<p>Appendix A. 179</p>
<p>Appendix B. 191</p>
<p>Appendix C. 211</p>
<p>Bibliography 225</p>
<p>Index 231</p>
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