Heritier, Stephane.
Robust Methods in Biostatistics. - 1st ed. - 1 online resource (294 pages) - Wiley Series in Probability and Statistics Ser. ; v.825 . - Wiley Series in Probability and Statistics Ser. .
Intro -- Robust Methods in Biostatistics -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- What is Robust Statistics? -- Against What is Robust Statistics Robust? -- Are Diagnostic Methods an Alternative to Robust Statistics? . -- How do Robust Statistics Compare with Other Statistical Procedures in Practice? -- 2 Key Measures and Results -- Introduction -- Statistical Tools for Measuring Robustness Properties -- The Influence Function -- The Breakdown Point -- Geometrical Interpretation -- The Rejection Point -- General Approaches for Robust Estimation -- The General Class of M-estimators -- Properties of M-estimators -- The Class of S-estimators -- Statistical Tools for Measuring Tests Robustness -- Sensitivity of the Two-sample t-test -- Local Stability of a Test: the Univariate Case -- Global Reliability of a Test: the Breakdown Functions -- General Approaches for Robust Testing -- Wald Test, Score Test and LRT -- Geometrical Interpretation -- General -type Classes of Tests -- Asymptotic Distributions -- Robustness Properties -- 3 Linear Regression -- Introduction -- Estimating the Regression Parameters -- The Regression Model -- Robustness Properties of the LS and MLE Estimators -- Glomerular Filtration Rate (GFR) Data Example -- Robust Estimators -- GFR Data Example (continued) -- Testing the Regression Parameters -- Significance Testing -- Diabetes Data Example -- Multiple Hypothesis Testing -- Diabetes Data Example (continued) -- Checking and Selecting the Model -- Residual Analysis -- GFR Data Example (continued) -- Diabetes Data Example (continued) -- Coefficient of Determination -- Global Criteria for Model Comparison -- Diabetes Data Example (continued) -- Cardiovascular Risk Factors Data Example -- 4 Mixed Linear Models -- Introduction -- The MLM -- The MLM Formulation -- Skin Resistance Data -- Semantic Priming Data. Orthodontic Growth Data -- Classical Estimation and Inference -- Marginal and REML Estimation -- Classical Inference -- Lack of Robustness of Classical Procedures -- Robust Estimation -- Bounded Influence Estimators -- S-estimators -- MM-estimators -- Choosing the Tuning Constants -- Skin Resistance Data (continued) -- Robust Inference -- Testing Contrasts -- Multiple Hypothesis Testing of the Main Effects -- Skin Resistance Data Example (continued) -- Semantic Priming Data Example (continued) -- Testing the Variance Components -- Checking the Model -- Detecting Outlying and Influential Observations -- Prediction and Residual Analysis -- Further Examples -- Metallic Oxide Data -- Orthodontic Growth Data (continued) -- Discussion and Extensions -- 5 Generalized Linear Models -- Introduction -- The GLM -- Model Building -- Classical Estimation and Inference for GLM -- Hospital Costs Data Example -- Residual Analysis -- A Class of M-estimators for GLMs -- Choice of ψ and w(x) -- Fisher Consistency Correction -- Nuisance Parameters Estimation -- IF and Asymptotic Properties -- Hospital Costs Example (continued) -- Robust Inference -- Significance Testing and CIs -- General Parametric Hypothesis Testing and Variable Selection -- Hospital Costs Data Example (continued) -- Breastfeeding Data Example -- Robust Estimation of the Full Model -- Variable Selection -- Doctor Visits Data Example -- Robust Estimation of the Full Model -- Variable Selection -- Discussion and Extensions -- Robust Hurdle Models for Counts -- Robust Akaike Criterion -- General Cp Criterion for GLMs -- Prediction with Robust Models -- 6 Marginal Longitudinal Data Analysis -- Introduction -- The Marginal Longitudinal Data Model (MLDA) and Alternatives -- Classical Estimation and Inference in MLDA -- Estimators for τ and α -- GUIDE Data Example -- Residual Analysis. A Robust GEE-type Estimator -- Linear Predictor Parameters -- Nuisance Parameters -- IF and Asymptotic Properties -- GUIDE Data Example (continued) -- Robust Inference -- Significance Testing and CIs -- Variable Selection -- GUIDE Data Example (continued) -- LEI Data Example -- Stillbirth in Piglets Data Example -- Discussion and Extensions -- 7 Survival Analysis -- Introduction -- The Cox Model -- The Partial Likelihood Approach -- Empirical Influence Function for the PLE -- Myeloma Data Example -- A Sandwich Formula for the Asymptotic Variance -- Robust Estimation and Inference in the Cox Model -- A Robust Alternative to the PLE -- Asymptotic Normality -- Handling of Ties -- Myeloma Data Example (continued) -- Robust Inference and its Current Limitations -- The Veteran's Administration Lung Cancer Data -- Robust Estimation -- Interpretation of the Weights -- Validation -- Structural Misspecifications -- Performance of the ARE -- Performance of the robust Wald test -- Other Issues -- Censored Regression Quantiles -- Regression Quantiles -- Extension to the Censored Case -- Asymptotic Properties and Robustness -- Comparison with the Cox Proportional Hazard Model -- Lung Cancer Data Example (continued) -- Limitations and Extensions -- Appendices -- A Starting Estimators for MM-estimators of Regression Parameters -- B Efficiency, LRT. , RAIC and RCp with Biweight .-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 -- Fisher Consistency Corrections -- Asymptotic Variance -- IRWLS Algorithm for Robust GLM -- F Computations for the Robust GEE Estimator -- IRWLS Algorithm for Robust GEE -- Fisher Consistency Corrections -- G Computation of the CRQ -- References -- Index.
"The authors are to be congratulated for providing consulting statisticians and advanced students of statistics with an excellent guide to the rich methodology now available. Every statistician will benefit from having this book on their shelf, or, better yet, on their desk." (Australian & New Zealand Journal of Statistics, 2011) "All treated methods are illustrated with several data examples. These data examples show clearly the superiority of the robust methods compared with the classical methods... However, since there exists a website with instructions for running the data examples of this book, the new robust methods can be easily applied." (Biometrical Journal, February 2011)"The book by Heritier et al. is the most comprehensive and practical discussion of robust methods to date. The combination of a summary of robust methods, extensive discussion of applications, and accompanying R code give this book the potential to increase the use of robust methods in practice." (Journal of Biopharmaceutical Statistics, March 2010).
9780470740545
Biomathematics.
Biometry -- Statistical methods.
Electronic books.
QH323.5.R615 2009
570.15195
Robust Methods in Biostatistics. - 1st ed. - 1 online resource (294 pages) - Wiley Series in Probability and Statistics Ser. ; v.825 . - Wiley Series in Probability and Statistics Ser. .
Intro -- Robust Methods in Biostatistics -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- What is Robust Statistics? -- Against What is Robust Statistics Robust? -- Are Diagnostic Methods an Alternative to Robust Statistics? . -- How do Robust Statistics Compare with Other Statistical Procedures in Practice? -- 2 Key Measures and Results -- Introduction -- Statistical Tools for Measuring Robustness Properties -- The Influence Function -- The Breakdown Point -- Geometrical Interpretation -- The Rejection Point -- General Approaches for Robust Estimation -- The General Class of M-estimators -- Properties of M-estimators -- The Class of S-estimators -- Statistical Tools for Measuring Tests Robustness -- Sensitivity of the Two-sample t-test -- Local Stability of a Test: the Univariate Case -- Global Reliability of a Test: the Breakdown Functions -- General Approaches for Robust Testing -- Wald Test, Score Test and LRT -- Geometrical Interpretation -- General -type Classes of Tests -- Asymptotic Distributions -- Robustness Properties -- 3 Linear Regression -- Introduction -- Estimating the Regression Parameters -- The Regression Model -- Robustness Properties of the LS and MLE Estimators -- Glomerular Filtration Rate (GFR) Data Example -- Robust Estimators -- GFR Data Example (continued) -- Testing the Regression Parameters -- Significance Testing -- Diabetes Data Example -- Multiple Hypothesis Testing -- Diabetes Data Example (continued) -- Checking and Selecting the Model -- Residual Analysis -- GFR Data Example (continued) -- Diabetes Data Example (continued) -- Coefficient of Determination -- Global Criteria for Model Comparison -- Diabetes Data Example (continued) -- Cardiovascular Risk Factors Data Example -- 4 Mixed Linear Models -- Introduction -- The MLM -- The MLM Formulation -- Skin Resistance Data -- Semantic Priming Data. Orthodontic Growth Data -- Classical Estimation and Inference -- Marginal and REML Estimation -- Classical Inference -- Lack of Robustness of Classical Procedures -- Robust Estimation -- Bounded Influence Estimators -- S-estimators -- MM-estimators -- Choosing the Tuning Constants -- Skin Resistance Data (continued) -- Robust Inference -- Testing Contrasts -- Multiple Hypothesis Testing of the Main Effects -- Skin Resistance Data Example (continued) -- Semantic Priming Data Example (continued) -- Testing the Variance Components -- Checking the Model -- Detecting Outlying and Influential Observations -- Prediction and Residual Analysis -- Further Examples -- Metallic Oxide Data -- Orthodontic Growth Data (continued) -- Discussion and Extensions -- 5 Generalized Linear Models -- Introduction -- The GLM -- Model Building -- Classical Estimation and Inference for GLM -- Hospital Costs Data Example -- Residual Analysis -- A Class of M-estimators for GLMs -- Choice of ψ and w(x) -- Fisher Consistency Correction -- Nuisance Parameters Estimation -- IF and Asymptotic Properties -- Hospital Costs Example (continued) -- Robust Inference -- Significance Testing and CIs -- General Parametric Hypothesis Testing and Variable Selection -- Hospital Costs Data Example (continued) -- Breastfeeding Data Example -- Robust Estimation of the Full Model -- Variable Selection -- Doctor Visits Data Example -- Robust Estimation of the Full Model -- Variable Selection -- Discussion and Extensions -- Robust Hurdle Models for Counts -- Robust Akaike Criterion -- General Cp Criterion for GLMs -- Prediction with Robust Models -- 6 Marginal Longitudinal Data Analysis -- Introduction -- The Marginal Longitudinal Data Model (MLDA) and Alternatives -- Classical Estimation and Inference in MLDA -- Estimators for τ and α -- GUIDE Data Example -- Residual Analysis. A Robust GEE-type Estimator -- Linear Predictor Parameters -- Nuisance Parameters -- IF and Asymptotic Properties -- GUIDE Data Example (continued) -- Robust Inference -- Significance Testing and CIs -- Variable Selection -- GUIDE Data Example (continued) -- LEI Data Example -- Stillbirth in Piglets Data Example -- Discussion and Extensions -- 7 Survival Analysis -- Introduction -- The Cox Model -- The Partial Likelihood Approach -- Empirical Influence Function for the PLE -- Myeloma Data Example -- A Sandwich Formula for the Asymptotic Variance -- Robust Estimation and Inference in the Cox Model -- A Robust Alternative to the PLE -- Asymptotic Normality -- Handling of Ties -- Myeloma Data Example (continued) -- Robust Inference and its Current Limitations -- The Veteran's Administration Lung Cancer Data -- Robust Estimation -- Interpretation of the Weights -- Validation -- Structural Misspecifications -- Performance of the ARE -- Performance of the robust Wald test -- Other Issues -- Censored Regression Quantiles -- Regression Quantiles -- Extension to the Censored Case -- Asymptotic Properties and Robustness -- Comparison with the Cox Proportional Hazard Model -- Lung Cancer Data Example (continued) -- Limitations and Extensions -- Appendices -- A Starting Estimators for MM-estimators of Regression Parameters -- B Efficiency, LRT. , RAIC and RCp with Biweight .-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 -- Fisher Consistency Corrections -- Asymptotic Variance -- IRWLS Algorithm for Robust GLM -- F Computations for the Robust GEE Estimator -- IRWLS Algorithm for Robust GEE -- Fisher Consistency Corrections -- G Computation of the CRQ -- References -- Index.
"The authors are to be congratulated for providing consulting statisticians and advanced students of statistics with an excellent guide to the rich methodology now available. Every statistician will benefit from having this book on their shelf, or, better yet, on their desk." (Australian & New Zealand Journal of Statistics, 2011) "All treated methods are illustrated with several data examples. These data examples show clearly the superiority of the robust methods compared with the classical methods... However, since there exists a website with instructions for running the data examples of this book, the new robust methods can be easily applied." (Biometrical Journal, February 2011)"The book by Heritier et al. is the most comprehensive and practical discussion of robust methods to date. The combination of a summary of robust methods, extensive discussion of applications, and accompanying R code give this book the potential to increase the use of robust methods in practice." (Journal of Biopharmaceutical Statistics, March 2010).
9780470740545
Biomathematics.
Biometry -- Statistical methods.
Electronic books.
QH323.5.R615 2009
570.15195