Robust multivariate classification procedures based on the mml estimators

Abstract

We develop a classification procedure based on Tiku's (1967, 1982) MML (modified maximum likelihood) estimators of location and scale parameters for classifying an observation in one of the two p-variate normal populations II1 and II2. We investigate the effects of non-normality on the errors of mis-classification e. and e1 and e2 and show that this new procedure is superior to the classical procedure (based on sample means and variances) and several other distribution-free procedures. The only assumption we make is that the marginal distributions of the underlying populations 111. and II2 have only two unknown parameters, the location and scale, and the means and variances of these marginal distributions exist. We also assume that II1 and II2 are identical other than a location shift.