An improved confidence ellipsoid for the linear regression model

Abstract

In a Monte Carlo experiment, we explore the coverage probability and volume of a percentile bootstrap confidence ellipsoid centered at the Stein-rule estimator of a multivariate normal mean. The ellipsoid we consider corresponds to the “improved-F” studied by Ullah, Carter, and Srivastava (1984, 1989) who have derived the small sigma and large-T asymptotic expansions of its distribution and studied the resulting approximations in a Monte Carlo setting. Unlike the Ullah et al. ellipsoid, the bootstrap ellipsoid covers the parameter point at or above nominal levels over large regions of the parameter space.