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 a region 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.

Key Words:

• Bounds with various shapes
• One-sided bounds
• p norm
• Projection methods
• Simultaneous tolerance bounds
• Taut bound