THE COVARIANCE ADJUSTED LOCATION LINEAR DISCRIMINANT FUNCTION FOR CLASSIFYING DATA WITH

UNEQUAL DISPERSION MATRICES IN DIFFERENT LOCATIONS

CHI-YING LEUNG

Department of Statistics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

(Received June 26, 1995; revised May 21, 1997)

Abstract. Classification between two populations dealing with both continuous and binary variables is handled by splitting the problem into different locations. Given the location specified by the values of the binary variables, discrimination is performed using the continuous variables. The location probability model with homoscedastic across location conditional dispersion matrices is adopted for this problem. In this paper, we consider presence of continuous covariates with heterogeneous location conditional dispersion matrices. The continuous covariates have equal location specific mean in both populations. Conditional homoscedasticity fails when strong interaction between the continuous and binary variables is present. A plug-in covariance adjusted rule is constructed and its asymptotic distribution is derived. An asymptotic expansion for the overall error rate is given. The result is extended to include binary covariates.

Key words and phrases: Location linear discriminant function, covariance adjustment, heteroscedastic conditional dispersion matrices, overall expected error rate.