Abstract
This paper is concerned with high-dimensional asymptotic results for W- and Z- rules when the sample size N and the dimension are large. Firstly, we give a unified location and scale mixture expression of the standard normal distribution for W and Z statistics. Then, the EPMCs (Expected Probability of Misclassifications) of W- and Z- rules are obtained in expanded forms with errors of It is pointed that Z-rule has smaller EER (Expected Error Rate) than W-rule when the prior probabilities are the same, neglecting the terms of Further, asymptotic unbiased estimators are proposed for the EPMCs and the EERs of W- and Z- rules. Accuracies of our asymptotic results are checked numerically by conducting a Mote Carlo simulation.
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