3 Large sample approximations and asymptotic expansions of classification statistics

Abstract

The distributions of classification statistics are needed mainly to know the Probability of Misclassification (PMC) or the probability of Correct Classification (PCC), an optimum choice of cut-off point, and to discuss on some testing hypotheses and estimations in the classification. Unfortunately, the exact distributions are usually hard to obtain. In the non-parametric classification, the distribution of classification statistics is usually based on the large samples. This chapter considers the distributions of classification statistics, such as statistics for classification of one of two multivariate normal populations with a common covariance matrix, statistics of classification into one of the two multivariate normal populations with different covariance matrices, and statistics in the non-normal case and in the discrete case.