Admissibility of the usual confidence interval in linear regression

TL;DR

This paper proves that the standard confidence interval for a linear combination of parameters in a linear regression model with normal errors is admissible among a wide class of confidence intervals.

Contribution

It establishes the admissibility of the usual confidence interval in linear regression for a broad class of intervals, confirming its optimality.

Findings

Usual confidence interval is admissible within a broad class.

Admissibility holds under normal error assumptions.

Supports the use of standard confidence intervals in practice.

Abstract

Consider a linear regression model with independent and identically normally distributed random errors. Suppose that the parameter of interest is a specified linear combination of the regression parameters. We prove that the usual confidence interval for this parameter is admissible within a broad class of confidence intervals.