Shinto Eguchi (Institute of Statistical Mathematics, Japan)

Maximization of a generalized t-statistic for linear discrimination in the two group classification problem

We discuss a statistical method for the classification problem with two groups labelled 0 and 1. We envisage a situation in which the conditional distribution given label 0 is well specified by a normal distribution, but the conditional distribution given label 1 is not well modelled by any specific distribution. Typically in a case-control study the distribution in the control group can be assumed to be normal, however the distribution in the case group may depart from normality. In this situation the maximum t-statistic for linear discrimination, or equivalently Fisher's linear discriminant function, may not be optiimal. We propose a class of generalized t-statistics and study asymptotic consistency and normality. The optimal generalized t-statistic in the sense of asymptotic variance is derived in a semi-parametric manner, and its statistical performance is confirmed in several numerical experiments.