An improved confidence region for the common mean vector of two multivariate homoscedastic normal distributions

Abstract

Consider the problem of estimating the common mean vector of two independent p - variate normal distributions with dispersion matrices and . For p=l the results regarding point estimation of the common mean have been obtained by many authors, Graybill and Deal (1959), Brown and Cohen (1974) , Bhattacharya (1981), recently Kubokawa (1987). A multivariate problem related to Linear Models has been considered by Khatri and Shah (1974). Norwood and Hinkelmann (1977) have proved result regarding common mean of several normal populations.

Brown and Cohen (1974) and Khatri and Shah (1981) have obtained an improved confidence interval for the common mean of univariate normal distribution. In this article we generalize a theorem of Brown and Cohen (1974) regarding interval estimation of the common mean to that of confidence region for the common mean vector of two p - variate homoscedastic normal populations. It is shown that the proposed confidence region has greater coverage probability than the usual confidence region based on the single sample.

Keywords:

• Confidence region
• P - variate normal distribution
• Coverage probability