Average-Width Optimality for Confidence Bands in Simple Linear Regression

Abstract

The problem of constructing optimal confidence bands for a simple linear regression over the whole real line is considered. Optimality is defined as minimization of the average width of the bands weighted by a normalized function. This weight function is presented as an indicator of experimental interest in the varying width of the band. A comparison between the commonly seen hyperbolic bands and segmented-line bands is presented.

Key Words:

• Simultaneous confidence intervals
• Prior weight functions
• Constrained minimization