Preliminary tests in linear discriminant analysis

Abstract

Let us consider k populations having p-variate normal distributions with a cammon variance-convariance matrix where the parameters are known. Let X denote the vector of observations on an axperimental unit, of which the origin is uncertain. The problem of allocating X to one of the k given populations is fundamental in multivariate analysis. In many applications , it is also interesting to determine whether X is related to a new population or not. This paper proposes a new test of typicality in linear discriminant analysis. simulation were performed to check the level and the power of the test when the mean and the variance have to be evaluated from the data.