Simultaneous Inference in Regression

Simultaneous confidence bands enable more intuitive and detailed inference of regression analysis than the standard inferential methods of parameter estimation and hypothesis testing. Simultaneous Inference in Regression provides a thorough overview of the construction methods and applications of simultaneous confidence bands for various inferential purposes. It supplies examples and MATLAB® programs that make it easy to apply the methods to your own data analysis. The MATLAB programs, along with color figures, are available for download on www.personal.soton.ac.uk/wl/mybook.html

Most of the book focuses on normal-error linear regression models. The author presents simultaneous confidence bands for a simple regression line, a multiple linear regression model, and polynomial regression models. He also uses simultaneous confidence bands to assess part of a multiple linear regression model with the zero function, to compare two regression models, and to evaluate more than two regression models. The final chapter demonstrates the use of simultaneous confidence bands in generalized linear regression models, such as logistic regression models.

This book shows how to employ simultaneous confidence bands to make useful inferences in regression analysis. The topics discussed can be extended to functions other than parametric regression functions, offering novel opportunities for research beyond linear regression models.

Wei Liu is a professor of statistics at the University of Southampton, UK. Dr. Liu has published more than 80 papers in peer-reviewed journals, including Annals of Statistics, Journal of the American Statistical Association, Journal of the Royal Statistical Society, Biometrika, and Biometrics. His research encompasses multiple comparison, simultaneous inference, and sequential methods.

Introduction to Linear Regression AnalysisLinear regression models Parameter estimation Testing hypotheses Confidence and prediction intervals

Confidence Bands for One Simple Regression Model PreliminariesHyperbolic bandsThree-segment bands Two-segment bands Other confidence bandsExtensions and restrictions of a confidence band Comparison of confidence bandsConfidence bands for percentiles and tolerance bands Bayesian simultaneous credible bands

Confidence Bands for One Multiple Regression ModelHyperbolic bands over the whole space Hyperbolic bands over a rectangular region Constant width bands over a rectangular regionHyperbolic bands over an ellipsoidal regionConstant-width bands over an ellipsoidal region Other confidence bands

Assessing Part of a Regression ModelPartial F test approach Hyperbolic confidence bands Assessing equivalence to the zero function

Comparison of Two Regression ModelsPartial F test approach Hyperbolic bands over the whole space Confidence bands over a rectangular regionConfidence bands over an ellipsoidal regionAssessing the equivalence of two models

Comparison of More Than Two Regression ModelsPartial F test approach Hyperbolic confidence bands for all contrastsBands for finite contrasts over rectangular region Bands for finite contrasts over ellipsoidal region Equivalence of more than two models

Confidence Bands for Polynomial RegressionConfidence bands for one model Confidence bands for part of a polynomial model Comparison of two polynomial models Comparison of more than two polynomial models

Confidence Bands for Logistic RegressionIntroduction to logistic regressionBands for one model Bands for comparing two models Bands for comparing more than two models
Appendix A: Approximation of the Percentile of a Random Variable Appendix B: Computation of Projection π (t,P,Xr) Appendix C: Computation of Projection π*(t,W,X2) Appendix D: Principle of Intersection-Union Test Appendix E: Computation of the K-Functions in Chapter 7
Bibliography
Index