Sharp Confidence Bands for Percentile Lines and Tolerance Bands for the Simple Linear Model

Abstract

This article develops sharp confidence bands for percentiles of regression functions over finite intervals. Attention is focused on one-sided (upper) bands for these percentiles, but a simple extension allows construction of two-sided bands. These upper bands are useful for tolerance bands, since a 100-γ percent confidence band for the 100/βth percentile is also a γ coefficient β-tolerance band.

Key Words:

• Confidence bands
• Percentiles
• Simultaneous inference
• General linear model
• Regression
• Tolerance bands