One-Sided Simultaneous Bounds in Linear Regression

Abstract

This article discusses the one-sided simultaneous tolerance and confidence bounds in the linear regression model. We approach the problem from the area of test theory. The bounds are constructed by projecting aregion of the test statistics, and we then propose a necessary and sufficient condition for obtaining a taut tolerance bound by the method. Finally, for illustrative purposes, we give several examples of one-sided simultaneous bounds with various shapes.