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.

当样本量N和维数较大时，本文关注W和Z规则的高维渐近结果。首先，我们给出W和Z统计量的标准正态分布的统一位置和比例混合表达式。然后，以展开形式获得W-和Z-规则的EPMC（错误分类的预期概率），误差为$Ø（{ñ}^{-2}）。$ 需要指出的是，当先验概率相同时，Z规则的EER（预期错误率）比W规则小。 $Ø（{ñ}^{-2}）。$此外，针对EPMC和W-和Z-规则的EER，提出了渐近无偏估计量。我们的渐近结果的准确性通过进行Mote Carlo模拟进行数值检查。