Simultaneous Inference in Regression

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 π (t,P,X_r)
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