An asymptotically-exact expression for the variance of classification error for the discrete histogram rule

Discrete classification is fundamental in GSP applications. In a previous publication, we provided analytical expressions for moments of the sampling distribution of the true error, as well as of resubstitution and leave-one-out error estimators, and their correlation with the true error, for the discrete histogram rule. When the number of samples or the total number of quantization levels is large, computation of these expression becomes difficult, and approximations must be made. In this paper, we provide an approximate expression for the variance of the classification error, which is shown to be asymptotically exact as the total number of quantization levels increases to infinity, under a mild distributional assumption.