Robust statistics for testing mean vectors of multivariate distributions

Abstract

We develop a ‘robust’ statistic T2 R, based on Tiku's (1967, 1980) MML (modified maximum likelihood) estimators of location and scale parameters, for testing an assumed meam vector of a symmetric multivariate distribution. We show that T2 R is one the whole considerably more powerful than the prominenet Hotelling T2 statistics. We also develop a robust statistic T2 D for testing that two multivariate distributions (skew or symmetric) are identical; T2 D seems to be usually more powerful than nonparametric statistics. The only assumption we make is that the marginal distributions are of the type (1/σk)f((x-μk)/σk) and the means and variances of these marginal distributions exist.