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High-dimensional asymptotic results for EPMCs of W- and Z- rules
Communications in Statistics - Theory and Methods ( IF 0.6 ) Pub Date : 2020-06-22
Takayuki Yamada, Tetsuro Sakurai, Yasunori Fujikoshi

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(N2). 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(N2). 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.



中文翻译:

W和Z规则的EPMC的高维渐近结果

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WZ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Øñ-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。 Øñ-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。

更新日期:2020-06-22
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