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.

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

Confidence Bands for One Simple Regression Model
Preliminaries
Hyperbolic bands
Three-segment bands
Two-segment bands
Other confidence bands
Extensions and restrictions of a confidence band
Comparison of confidence bands
Confidence bands for percentiles and tolerance bands
Bayesian simultaneous credible bands

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

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

Comparison of Two Regression Models
Partial F test approach
Hyperbolic bands over the whole space
Confidence bands over a rectangular region
Confidence bands over an ellipsoidal region
Assessing the equivalence of two models

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

Confidence Bands for Polynomial Regression
Confidence 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 Regression
Introduction to logistic regression
Bands 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 p (t,P,X_r)
Appendix C: Computation of Projection p*(t,W,X₂)
Appendix D: Principle of Intersection-Union Test
Appendix E: Computation of the K-Functions in Chapter 7

Bibliography

Index

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.