Robust statistics is an extension of classical statistics that specifically takes into account the concept that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable when the data do not exactly match the postulated models as it is the case for example with outliers. Robust Methods in Biostatistics proposes robust alternatives to common methods used in statistics in general and in biostatistics in particular and illustrates their use on many biomedical datasets. The methods introduced include robust…mehr
Robust statistics is an extension of classical statistics that specifically takes into account the concept that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable when the data do not exactly match the postulated models as it is the case for example with outliers.
Robust Methods in Biostatistics proposes robust alternatives to common methods used in statistics in general and in biostatistics in particular and illustrates their use on many biomedical datasets. The methods introduced include robust estimation, testing, model selection, model check and diagnostics. They are developed for the following general classes of models:
Linear regression Generalized linear models Linear mixed models Marginal longitudinal data models Cox survival analysis model
The methods are introduced both at a theoretical and applied level within the framework of each general class of models, with a particular emphasis put on practical data analysis. This book is of particular use for research students,applied statisticians and practitioners in the health field interested in more stable statistical techniques. An accompanying website provides R code for computing all of the methods described, as well as for analyzing all the datasets used in the book.
Dr Stephane Heritier, NHMRC Clinical Trials Centre, University of Sydney, Australia. A senior lecturer in statistics for four years, Dr Heritier also has over a decade of research to her name, and has published numerous articles in a variety of journals. Dr Eva Cantoni, Department of Econometrics, University of Geneva, Switzerland. Also a senior lecturer in statistics, Dr Cantoni has many years teaching and research experience, and written a number journal articles. Dr Samuel Copt, NHMRC Clinical Trials Centre, University of Sydney, Australia. Having completed his PhD in 2004, Dr Copt has already spent a year as a lecturer and published six journal articles. He is now a visiting scholar at the University of Sydney. Professor Maria-Pia Victoria-Feser, HEC Section, University of Geneva, Switzerland. Professor Victoria-Feser has over 10 years of teaching experience and has written many journal articles.
Inhaltsangabe
Preface. Acknowledgments. 1 Introduction. 1.1 What is Robust Statistics? 1.2 Against What is Robust Statistics Robust? 1.3 Are Diagnostic Methods an Alternative to Robust Statistics? 1.4 How do Robust Statistics Compare with Other Statistical Procedures in Practice? 2 Key Measures and Results. 2.1 Introduction. 2.2 Statistical Tools for Measuring Robustness Properties. 2.3 General Approaches for Robust Estimation. 2.4 Statistical Tools for Measuring Tests Robustness. 2.5 General Approaches for Robust Testing. 3 Linear Regression. 3.1 Introduction. 3.2 Estimating the Regression Parameters. 3.3 Testing the Regression Parameters. 3.4 Checking and Selecting the Model. 3.5 CardiovascularRiskFactorsDataExample. 4 Mixed Linear Models. 4.1 Introduction. 4.2 The MLM. 4.3 Classical Estimation and Inference. 4.4 Robust Estimation. 4.5 Robust Inference. 4.6 Checking the Model. 4.7 Further Examples. 4.8 Discussion and Extensions. 5 Generalized Linear Models. 5.1 Introduction. 5.2 The GLM. 5.3 A Class of M-estimators forGLMs. 5.4 Robust Inference. 5.5 Breastfeeding Data Example. 5.6 Doctor Visits Data Example. 5.7 Discussion and Extensions. 6 Marginal Longitudinal Data Analysis. 6.1 Introduction. 6.2 The Marginal Longitudinal Data Model (MLDA) and Alternatives. 6.3 A Robust GEE-type Estimator. 6.4 Robust Inference. 6.5 LEI Data Example. 6.6 Stillbirth in Piglets Data Example. 6.7 Discussion and Extensions. 7 Survival Analysis. 7.1 Introduction. 7.2 TheCox Model. 7.3 Robust Estimation and Inference in the Cox Model. 7.4 The Veteran's Administration Lung Cancer Data. 7.5 Structural Misspecifications. 7.6 Censored Regression Quantiles. Appendices. A Starting Estimators for MM-estimators of Regression Parameters. B Efficiency, LRTÁ , RAIC and RCp with Biweight Á-function for the Regression Model. C An Algorithm Procedure for the Constrained S-estimator. D Some Distributions of the Exponential Family. E Computations for the Robust GLM Estimator. E.1 Fisher Consistency Corrections. E.2 Asymptotic Variance. E.3 IRWLS Algorithm for Robust GLM. F Computations for the Robust GEE Estimator. F.1 IRWLS Algorithm for Robust GEE. F.2 Fisher Consistency Corrections. G Computation of the CRQ. References. Index.
Preface. Acknowledgments. 1 Introduction. 1.1 What is Robust Statistics? 1.2 Against What is Robust Statistics Robust? 1.3 Are Diagnostic Methods an Alternative to Robust Statistics? 1.4 How do Robust Statistics Compare with Other Statistical Procedures in Practice? 2 Key Measures and Results. 2.1 Introduction. 2.2 Statistical Tools for Measuring Robustness Properties. 2.3 General Approaches for Robust Estimation. 2.4 Statistical Tools for Measuring Tests Robustness. 2.5 General Approaches for Robust Testing. 3 Linear Regression. 3.1 Introduction. 3.2 Estimating the Regression Parameters. 3.3 Testing the Regression Parameters. 3.4 Checking and Selecting the Model. 3.5 CardiovascularRiskFactorsDataExample. 4 Mixed Linear Models. 4.1 Introduction. 4.2 The MLM. 4.3 Classical Estimation and Inference. 4.4 Robust Estimation. 4.5 Robust Inference. 4.6 Checking the Model. 4.7 Further Examples. 4.8 Discussion and Extensions. 5 Generalized Linear Models. 5.1 Introduction. 5.2 The GLM. 5.3 A Class of M-estimators forGLMs. 5.4 Robust Inference. 5.5 Breastfeeding Data Example. 5.6 Doctor Visits Data Example. 5.7 Discussion and Extensions. 6 Marginal Longitudinal Data Analysis. 6.1 Introduction. 6.2 The Marginal Longitudinal Data Model (MLDA) and Alternatives. 6.3 A Robust GEE-type Estimator. 6.4 Robust Inference. 6.5 LEI Data Example. 6.6 Stillbirth in Piglets Data Example. 6.7 Discussion and Extensions. 7 Survival Analysis. 7.1 Introduction. 7.2 TheCox Model. 7.3 Robust Estimation and Inference in the Cox Model. 7.4 The Veteran's Administration Lung Cancer Data. 7.5 Structural Misspecifications. 7.6 Censored Regression Quantiles. Appendices. A Starting Estimators for MM-estimators of Regression Parameters. B Efficiency, LRTÁ , RAIC and RCp with Biweight Á-function for the Regression Model. C An Algorithm Procedure for the Constrained S-estimator. D Some Distributions of the Exponential Family. E Computations for the Robust GLM Estimator. E.1 Fisher Consistency Corrections. E.2 Asymptotic Variance. E.3 IRWLS Algorithm for Robust GLM. F Computations for the Robust GEE Estimator. F.1 IRWLS Algorithm for Robust GEE. F.2 Fisher Consistency Corrections. G Computation of the CRQ. References. Index.
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