Buch, Englisch, 432 Seiten, Format (B × H): 155 mm x 236 mm, Gewicht: 771 g
Buch, Englisch, 432 Seiten, Format (B × H): 155 mm x 236 mm, Gewicht: 771 g
ISBN: 978-1-84821-619-8
Verlag: Wiley
Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical Models and Methods in Survival Analysis, and Reliability and Maintenance.
The book is intended for researchers interested in statistical methodology and models useful in survival analysis, system reliability and statistical testing for censored and non-censored data.
Autoren/Hrsg.
Weitere Infos & Material
Preface xv
Biography of Mikhail Stepanovitch Nikouline xvii
Vincent COUALLIER, Léo GERVILLE-RÉACHE, Catherine HUBER-CAROL, Nikolaos LIMNIOS and Mounir MESBAH
Part 1. Statistical Models and Methods 1
Chapter 1. Unidimensionality, Agreement and Concordance Probability 3
Zhezhen JIN and Mounir MESBAH
1.1. Introduction 3
1.2. From reliability to unidimensionality: CAC and curve 4
1.2.1. Classical unidimensional models for measurement 4
1.2.2. Reliability of an instrument: CAC 6
1.2.3. Unidimensionality of an instrument: BRC 9
1.3. Agreement between binary outcomes: the kappa coefficient 10
1.3.1. The kappa model 10
1.3.2. The kappa coefficient 10
1.3.3. Estimation of the kappa coefficient 10
1.4. Concordance probability 11
1.4.1. Relationship with Kendall’s t measure 12
1.4.2. Relationship with Somer’s D measure 12
1.4.3. Relationship with ROC curve 13
1.5. Estimation and inference 14
1.6. Measure of agreement 14
1.7. Extension to survival data 15
1.7.1. Harrell’s c-index 15
1.7.2. Measure of discriminatory power 16
1.8. Discussion 17
1.9. Bibliography 18
Chapter 2. A Universal Goodness-of-Fit Test Based on Regression Techniques 21
Florence GEORGE and Sneh GULATI
2.1. Introduction 21
2.2. The Brain and Shapiro procedure for the exponential distribution 22
2.3. Applications of the Brain and Shapiro test 24
2.4. Small sample null distribution of the test statistic for specific distributions 25
2.5. Power studies 28
2.6. Some real examples 28
2.7. Conclusions 31
2.8. Acknowledgment 32
2.9. Bibliography 32
Chapter 3. Entropy-type Goodness-of-Fit Tests for Heavy-Tailed Distributions 33
Andreas MAKRIDES, Alex KARAGRIGORIOU and Filia VONTA
3.1. Introduction 33
3.2. The entropy test for heavy-tailed distributions 35
3.2.1. Development and asymptotic theory 35
3.2.2. Discussion 39
3.3. Simulation study 40
3.4. Conclusions 42
3.5. Bibliography 42
Chapter 4. Penalized Likelihood Methodology and Frailty Models 45
Emmanouil ANDROULAKIS, Christos KOUKOUVINOS and Filia VONTA
4.1. Introduction 45
4.2. Penalized likelihood in frailty models for clustered data 48
4.2.1. Gamma distributed frailty 52
4.2.2. Inverse Gaussian distributed frailty 52
4.2.3. Uniform distributed frailty 54
4.3. Simulation results 55
4.4. Concluding remarks 57
4.5. Bibliography 57
Chapter 5. Interactive Investigation of Statistical Regularities in Testing Composite Hypotheses of Goodness of Fit 61
Boris LEMESHKO, Stanislav LEMESHKO and Andrey ROGOZHNIKOV
5.1. Introduction 61
5.2. Distributions of the test statistics in the case of testing composite hypotheses 63
5.3. Testing composite hypotheses in “real-time” 68
5.4. Conclusions 73
5.5. Acknowledgment 73
5.6. Bibliography 73
Chapter 6. Modeling of Categorical Data 77
Henning LÄUTER
6.1. Introduction 77
6.2. Continuous conditional distributions 78
6.2.1. Conditional normal distribution 78
6.2.1.1. Estimation of parameters 78
6.2.2. More general continuous conditional distributions 81
6.2.2.1. Conditional distribution 82
6.2.2.2. Normal copula 83
6.3. Discrete conditional distributions 84
6.3.1. Parametric conditional distributions 84
6.3.2. Estimation of parameters 86
6.4. Goodness of fit 86
6.4.1. Distribution of ˆX2 87
6.5. Modeling of categorical data 88
6.5.1. Contingency tables 89
6.5.1.1. General tables 89
6.5.1.2. Further examples 93
6.6. Bibliography 93
Chapter 7. Within the Sample Comparison of Prediction Performance of Models and Submodels: Application to Alzheimer’s Disease 95
Catherine HUBER-CAROL, Shulamith T. GROSS and Annick ALPÉROVITCH
7.1. Introduction 95
7.2. Framework 96
7.2.1. General description of the data set and the models to be compared 96
7.2.2. Definition of the performance prediction criteria: IDI and BRI 96
7.3. Estimation of IDI and BRI 97
7.3.1. General estimating equations for IDI and BRI 98
7.3.2. Estimation of IDI and BRI in the logistic case 98
7.3.2.1. Asymptotics of IDI2/1 for logistic predictors 99
7.3.2.2. Asymptotics of BRI2/1 for logistic predictors 100
7.4. Simulation studies 102
7.4.1. First simulation 102
7.4.2. Second simulation: Gu and Pepe’s example 104
7.5. The three city study of Alzheimer’s disease 106
7.6. Conclusion 108
7.7. Bibliography 109
Chapter 8. Durbin–Knott Components and Transformations of the Cramér-von Mises Test 111
Gennady MARTYNOV
8.1. Introduction 111
8.2. Weighted Cramér-von Mises statistic 111
8.3. Examples of the Cramér-von Mises statistics 113
8.3.1. Classical Cramér-von Mises statistic 113
8.3.2. Anderson–Darling statistic 113
8.3.3. Cramér-von Mises statistic with the power weight function 114
8.4. Weighted parametric Cramér-von Mises statistic 114
8.4.1. Covariance functions of weighted parametric empirical process 114
8.4.2. Eigenvalues and eigenfunctions for weighted parametric Cramérvon Mises statistic 116
8.5. Transformations of the Cramér-von Mises statistic 117
8.5.1. Preliminary notes 117
8.5.2. Replacement of eigenvalues 118
8.5.3. Transformed statistics 119
8.6. Bibliography 122
Chapter 9. Conditional Inference in Parametric Models 125
Michel BRONIATOWSKI and Virgile CARON
9.1. Introduction and context 125
9.2. The approximate conditional density of the sample 127
9.2.1. Approximation of conditional densities 127
9.2.2. The proxy of the conditional density of the sample 129
9.2.3. Comments on implementation 131
9.3. Sufficient statistics and approximated conditional density 131
9.3.1. Keeping sufficiency under the proxy density 131
9.3.2. Rao–Blackwellization 132
9.4. Exponential models with nuisance parameters 135
9.4.1. Conditional inference in exponential families 135
9.4.2. Application of conditional sampling to MC tests 137
9.4.2.1. Context 137
9.4.2.2. Bimodal likelihood: testing the mean of a normal distribution in dimension 2 139
9.4.3. Estimation through conditional likelihood 140
9.5. Bibliography 142
Chapter 10. On Testing Stochastic Dominance by Exceedance, Precedence and Other Distribution-Free Tests, with Applications 145
Paul DEHEUVELS
10.1. Introduction 145
10.2. Results 148
10.2.1. The experimental data set 148
10.2.2. An application of the Wilcoxon–Mann–Whitney statistics 149
10.2.3. One-sided Kolmogorov-Smirnov tests 150
10.2.4. Precedence and Exceedance Tests. 152
10.3. Negative binomial limit laws 155
10.4. Conclusion 159
10.5. Bibliography 159
Chapter 11. Asymptotically Parameter-Free Tests for Ergodic Diffusion Processes 161
Yury A. KUTOYANTS and Li ZHOU
11.1. Introduction 161
11.2. Ergodic diffusion process and some limits 165
11.3. Shift parameter 168
11.4. Shift and scale parameters 172
11.5. Bibliography 175
Chapter 12. A Comparison of Homogeneity Tests for Different Alternative Hypotheses 177
Sergey POSTOVALOV and Petr PHILONENKO
12.1. Homogeneity tests 178
12.1.1. Tests for data without censoring 179
12.1.2. Tests for data with censoring 180
12.2. Alternative hypotheses 184
12.3. Power simulation 185
12.3.1. Power of tests without censoring
