Fixed–size confidence regions for the mean vector of a multinormal distribution

In this paper we propose two stage, modified two stage purely sequential, and three stage procedures to construct "fixed size" elliptic confidence regions for estimating the mean vector of a p–dimensional normal distribution when the dispersion matrix is of the form σ2H where σ ∊(0,∞) and H is a p x p known positive definite matrix.We feel that the modified two-stage procedure can be almost as good as the three-stage procedure. In some applications, our modified two-stage procedure may be more appealing than the implementation of a three-stage scheme. So, our findings may possibly limit the usefulness of the three-stage sampling in some of the practical applications. Results and tools from Mukhopadhyay (1974, 1980, 1981), Ghosh and Mukhopadhyay (1975, 1976, 1979, 1981),Srivastava (1967),Woodroofe (1977),and Hall (1981) have been found to be extremely important and useful in this present study. We report extensive simulation studies in order to be able to put the competitive procedures in their proper perspectives.