Construction of exact simultaneous confidence bands in multiple linear regression with predictor variables constrained in an ellipsoidal region

Description/Abstract

A simultaneous confidence band provides useful information on the plausible range of the unknown regression model. There are several recent papers using confidence bands for various inferential purposes; see, for example, Sun, Raz and Faraway (1999), Spurrier (1999), Al-Saidy et al. (2003), Liu, Jamshidian and Zhang (2004), and Piegorsch et al. (2005). Construction of simultaneous confidence bands has a history going back to Working and Hotelling (1929), and is often a hard problem when the region over which a confidence band is required is restricted and the number of predictor variables is more than one. This article considers the construction of exact level one-sided and two-sided simultaneous confidence bands of hyperbolic shape for the normal-error multiple linear regression model when the predictor variables are constrained to a particular ellipsoidal region that is centered at the point of the means of the predictor variable values used in the experiment. MATLAB programs have been written for easy implementation of the constructions, and an illustrative example is provided.