TEST FOR EQUALITY OF MEAN VECTORS AND PROFILE ANALYSIS

Abstract

In this paper, we consider some procedures of testing equality of mean vectors and of profile analysis under elliptical populations having correlation among them. Hotelling's T^2 type statistic is important for testing equality of mean vectors and is discussed in normal and non-normal populations by many authors. Test for equality of mean vectors in multivariate normal populations which have correlation among populations is introduced by Morrison (2005). This test statistic is usually called Paired T^2 statistic, which is Hotelling's T^2 type statistic. In order to consider testing the equality of the mean vectors and construct the simultaneous confidence intervals, we derive the approximate upper percentiles for the distribution of the paired T^2 statistic. Moreover, we consider the profile analysis using Hotelling's T^2 type statistics. Profile analysis in elliptical populations is discussed by Okamoto et al. (2006) and so on. We derive the approximate upper percentiles in elliptical populations with correlation. Finally, the accuracy of the approximate values for Paired T^2 type statistics and Hotelling's T^2 type statistic for profile analysis is investigated by Monte Carlo simulations for selected values of parameters.