Computable error bounds for asymptotic approximations of the quadratic discriminant function

Abstract

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.