Computable error bounds for asymptotic approximations of the quadratic discriminant function

Abstract

A bstract . This paper is concerned with computable error bounds for asymptotic approximations of the expected probabilities of misclassification (EPMC) of the quadratic discriminant function Q . A location and scale mixture expression for Q is given as a special case of a general discriminant function including the linear and quadratic discriminant functions. Using the result, we provide computable error bounds for asymptotic approximations of the EPMC of Q when both the sample size and the dimensionality are large. The bounds are numerically explored. Similar results are given for a quadratic discriminant function Q 0 when the covariance matrix is known.