A Robust Test in the Multivariate Two-Sample Location Problem

SYNOPTIC ABSTRACT

A frequently employed test for the equality of two mean vectors is Hotelling's two-sample T², which assumes multinormality of the populations. When the multinormality assumption is violated, modified versions of T² and/or nonparametric statistics are utilized. In this paper, it is shown that if Hotelling's T² statistic is computed as a function of the ranks (instead of the original observations), the resulting statistic is a monotone function of a nonparametric statistic. Just as T² reduces to the square of a t-statistic in univariate distributions, the rank T² reduces to a rank transform statistic T_R proposed by Conover and Iman (1981). For several bivariate distributions, Monte Carlo results are presented, which suggest robustness of rank T².

Key Words and Phrases:

• rank transformation
• Hotelling's T²
• Monte Carlo simulation
• location problem