On the Non-Existence of a Fixed-Volume Confidence Ellipsoid for Multinormal Mean

Abstract

It is well known (Dantzig, 1940) that based on a sample of given size from a univariate normal distribution with all unknown parameters, there does not exist a confidence interval for the mean with a preassigned length and a positive confidence coefficient. In this article we extend this result to the case of a multivariate normal population following a more direct approach recently considered by Lehmann (1986).