Estimating the Conditional Probability of Misclassification

Abstract

Let x be an observation assumed to be from one of two p-dimensional normal populations II, II2 with unknown mean vectors t , t2 and common known covariance matrix M. The observation is to be classified as coming from one of the populations. Samples S1 , S2 consisting of N1 , N2 observations known to come from HI , II2 respectively are also available, and a classification rule is based on these samples. This paper is concerned with the problem of estimating the conditional probability of misclassifying x given a fixed classification rule. Let xi , x2i (i = 1, ... , N ; j = 1, *. , N2) denote the observations in S1, S2, and let i , 22 denote the sample means. The classification rule will be the commonly used one (see for example Anderson, (1958)) that classifies x as HII if