Liu W. Simultaneous Inference in Regression

CRC Press, Taylor & Francis Group, 2011. — 269 p. — ISBN: 978-1439828090.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.
Appendices.