Confidence Sets for the Mean of a Multivariate Normal Distribution

Abstract

SUMMARY An attempt is made to determine confidence sets for the mean of a multivariate normal distribution with known covariance matrix that take advantage of the fact that the sample mean is not the best estimate when the loss is a non-singular quadratic function of the error vector. Only the case of high dimension is considered. The geometrical size and shape of the confidence sets, the probability of covering false values, and the relation to posterior probabilities are studied, unfortunately somewhat incompletely.