Robust methods in biostatistics:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Chichester
Wiley
2009
|
| Edition: | 1. publ. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 249 - 264 |
| Physical Description: | XIV, 268 S. graph. Darst. 24 cm |
| ISBN: | 9780470027264 0470027266 |
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| 245 | 1 | 0 | |a Robust methods in biostatistics |c Stephane Heritier ... |
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Record in the Search Index
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| adam_text | Titel: Robust methods in biostatistics
Autor: Heritier, Stephane
Jahr: 2009
Contents
Preface xiii
Acknowledgments xv
1 Introduction 1
1.1 What is Robust Statistics? 1
1.2 Against What is Robust Statistics Robust? 3
1.3 Are Diagnostic Methods an Alternative to Robust Statistics? .... 7
1.4 How do Robust Statistics Compare with Other Statistical Procedures
in Practice? 11
2 Key Measures and Results 15
2.1 Introduction 15
2.2 Statistical Tools for Measuring Robustness Properties 16
2.2.1 The Influence Function 17
2.2.2 The Breakdown Point 20
2.2.3 Geometrical Interpretation 20
2.2.4 The Rejection Point 21
2.3 General Approaches for Robust Estimation 21
2.3.1 The General Class of M-estimators 23
2.3.2 Properties of M-estimators 27
2.3.3 The Class of S-estimators 30
2.4 Statistical Tools for Measuring Tests Robustness 32
2.4.1 Sensitivity of the Two-sample/ -test 34
2.4.2 Local Stability of a Test: the Univariate Case 34
2.4.3 Global Reliability of a Test: the Breakdown Functions ... 37
2.5 General Approaches for Robust Testing 38
2.5.1 Wald Test, Score Test and LRT 39
2.5.2 Geometrical Interpretation 40
2.5.3 General*-type Classes of Tests 40
2.5.4 Asymptotic Distributions 42
2.5.5 Robustness Properties 43
viii CONTENTS
3 Linear Regression 45
3.1 Introduction 45
3.2 Estimating the Regression Parameters 47
3.2.1 The Regression Model 47
3.2.2 Robustness Properties of the LS and MLE Estimators . ... 48
3.2.3 Glomerular Filtration Rate (GFR) Data Example 49
3.2.4 Robust Estimators 50
3.2.5 GFR Data Example (continued) 54
3.3 Testing the Regression Parameters 55
3.3.1 Significance Testing 55
3.3.2 Diabetes Data Example 58
3.3.3 Multiple Hypothesis Testing 59
3.3.4 Diabetes Data Example (continued) 61
3.4 Checking and Selecting the Model 62
3.4.1 Residual Analysis 62
3.4.2 GFR Data Example (continued) 62
3.4.3 Diabetes Data Example (continued) 65
3.4.4 Coefficient of Determination 66
3.4.5 Global Criteria for Model Comparison 69
3.4.6 Diabetes Data Example (continued) 75
3.5 Cardiovascular Risk Factors Data Example 78
4 Mixed Linear Models 83
4.1 Introduction 83
4.2 TheMLM 84
4.2.1 The MLM Formulation 84
4.2.2 Skin Resistance Data 88
4.2.3 Semantic Priming Data 89
4.2.4 Orthodontic Growth Data 90
4.3 Classical Estimation and Inference 91
4.3.1 Marginal and REML Estimation 91
4.3.2 Classical Inference 94
4.3.3 Lack of Robustness of Classical Procedures 96
4.4 Robust Estimation 97
4.4.1 Bounded Influence Estimators 97
4.4.2 S-estimators 98
4.4.3 MA/-estimators 100
4.4.4 Choosing the Tuning Constants 102
4.4.5 Skin Resistance Data (continued) 103
4.5 Robust Inference 104
4.5.1 Testing Contrasts 104
4.5.2 Multiple Hypothesis Testing of the Main Effects 106
4.5.3 Skin Resistance Data Example (continued) 107
4.5.4 Semantic Priming Data Example (continued) 107
4.5.5 Testing the Variance Components 110
CONTENTS ix
4.6 Checking the Model 110
4.6.1 Detecting Outlying and Influential Observations 110
4.6.2 Prediction and Residual Analysis 112
4.7 Further Examples 116
4.7.1 Metallic Oxide Data 116
4.7.2 Orthodontic Growth Data (continued) 118
4.8 Discussion and Extensions 122
5 Generalized Linear Models 125
5.1 Introduction 125
5.2 TheGLM 126
5.2.1 Model Building 126
5.2.2 Classical Estimation and Inference for GLM 129
5.2.3 Hospital Costs Data Example 132
5.2.4 Residual Analysis 133
5.3 A Class of A/-estimators for GLMs 136
5.3.1 Choice of V and w(x) 137
5.3.2 Fisher Consistency Correction 138
5.3.3 Nuisance Parameters Estimation 139
5.3.4 IF and Asymptotic Properties 140
5.3.5 Hospital Costs Example (continued) 140
5.4 Robust Inference 141
5.4.1 Significance Testing and CIs 141
5.4.2 General Parametric Hypothesis Testing and
Variable Selection 142
5.4.3 Hospital Costs Data Example (continued) 144
5.5 Breastfeeding Data Example 146
5.5.1 Robust Estimation of the Full Model 146
5.5.2 Variable Selection 148
5.6 Doctor Visits Data Example 151
5.6.1 Robust Estimation of the Full Model 151
5.6.2 Variable Selection 154
5.7 Discussion and Extensions 158
5.7.1 Robust Hurdle Models for Counts 158
5.7.2 Robust Akaike Criterion 159
5.7.3 General Cp Criterion for GLMs 159
5.7.4 Prediction with Robust Models 160
6 Marginal Longitudinal Data Analysis 161
6.1 Introduction 161
6.2 The Marginal Longitudinal Data Model (MLDA) and Alternatives . 163
6.2.1 Classical Estimation and Inference in MLDA 164
6.2.2 Estimators for r and a 166
6.2.3 GUIDE Data Example 169
6.2.4 Residual Analysis 171
x CONTENTS
6.3 A Robust GEE-type Estimator 172
6.3.1 Linear Predictor Parameters 172
6.3.2 Nuisance Parameters 174
6.3.3 IF and Asymptotic Properties 176
6.3.4 GUIDE Data Example (continued) 177
6.4 Robust Inference 178
6.4.1 Significance Testing and CIs 178
6.4.2 Variable Selection 179
6.4.3 GUIDE Data Example (continued) 180
6.5 LEI Data Example 182
6.6 Stillbirth in Piglets Data Example 186
6.7 Discussion and Extensions 189
7 Survival Analysis 191
7.1 Introduction 191
7.2 The Cox Model 193
7.2.1 The Partial Likelihood Approach 193
7.2.2 Empirical Influence Function for the PLE 196
7.2.3 Myeloma Data Example 197
7.2.4 A Sandwich Formula for the Asymptotic Variance 198
7.3 Robust Estimation and Inference in the Cox Model 200
7.3.1 A Robust Alternative to the PLE 200
7.3.2 Asymptotic Normality 202
7.3.3 Handling of Ties 204
7.3.4 Myeloma Data Example (continued) 205
7.3.5 Robust Inference and its Current Limitations 206
7.4 The Veteran s Administration Lung Cancer Data 209
7.4.1 Robust Estimation 209
7.4.2 Interpretation of the Weights 210
7.4.3 Validation 212
7.5 Structural Misspecifications 214
7.5.1 Performance of the ARE 214
7.5.2 Performance of the robust Wald test 216
7.5.3 Other Issues 217
7.6 Censored Regression Quantiles 217
7.6.1 Regression Quantiles 217
7.6.2 Extension to the Censored Case 219
7.6.3 Asymptotic Properties and Robustness 220
7.6.4 Comparison with the Cox Proportional Hazard Model ... 221
7.6.5 Lung Cancer Data Example (continued) 222
7.6.6 Limitations and Extensions 224
CONTENTS xi
Appendices 227
A Starting Estimators for MM -estimators of Regression Parameters 229
B Efficiency, LRT^, RAIC and RCP with Biweight /o-function for
the Regression Model 231
C An Algorithm Procedure for the Constrained S-estimator 235
D Some Distributions of the Exponential Family 237
E Computations for the Robust GLM Estimator 239
E. 1 Fisher Consistency Corrections 239
E.2 Asymptotic Variance 240
E.3 IRWLS Algorithm for Robust GLM 242
F Computations for the Robust GEE Estimator 245
F.I IRWLS Algorithm for Robust GEE 245
F.2 Fisher Consistency Corrections 246
G Computation of the CRQ 247
References 249
Index 265
|
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| discipline | Biologie Mathematik |
| edition | 1. publ. |
| format | Book |
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| spelling | Robust methods in biostatistics Stephane Heritier ... 1. publ. Chichester Wiley 2009 XIV, 268 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Literaturverz. S. 249 - 264 Biometry Statistical methods Biometry methods Biostatistik (DE-588)4729990-3 gnd rswk-swf Robuste Statistik (DE-588)4451047-0 gnd rswk-swf Biostatistik (DE-588)4729990-3 s DE-604 Robuste Statistik (DE-588)4451047-0 s Heritier, Stéphane Sonstige (DE-588)17169144X oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018722128&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robust methods in biostatistics Biometry Statistical methods Biometry methods Biostatistik (DE-588)4729990-3 gnd Robuste Statistik (DE-588)4451047-0 gnd |
| subject_GND | (DE-588)4729990-3 (DE-588)4451047-0 |
| title | Robust methods in biostatistics |
| title_auth | Robust methods in biostatistics |
| title_exact_search | Robust methods in biostatistics |
| title_full | Robust methods in biostatistics Stephane Heritier ... |
| title_fullStr | Robust methods in biostatistics Stephane Heritier ... |
| title_full_unstemmed | Robust methods in biostatistics Stephane Heritier ... |
| title_short | Robust methods in biostatistics |
| title_sort | robust methods in biostatistics |
| topic | Biometry Statistical methods Biometry methods Biostatistik (DE-588)4729990-3 gnd Robuste Statistik (DE-588)4451047-0 gnd |
| topic_facet | Biometry Statistical methods Biometry methods Biostatistik Robuste Statistik |
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