Maximization of the Generalized t-Statistics for Two-class Discrimination Problem

Abstract

Maximization of the Generalized t-Statistics for Two-class Discrimination Problem Osamu Komori The Institute of Statistical Mathematics, Japan. ?: 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 via an appropriate data transformation, however the distribution in the case group may depart from normality. In this situation the maximum t-statistic for linear discrimination, or equivalently Fisher linear discriminant function, may not be optimal. 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.