High-dimensional asymptotic results for EPMCs of W- and Z- rules

Takayuki Yamada, Tetsuro Sakurai and Yasunori Fujikoshi

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 8, 2385-2413

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 O(N−2). 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 O(N−2). 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.

Date: 2022
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DOI: 10.1080/03610926.2020.1774060

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