On the Distributions of some Test Statistics for Profile Analysis in Elliptical Populations
On the Distributions of some Test Statistics for Profile Analysis in Elliptical Populations
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DOI：
10.1080/01966324.2006.10737659
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发表时间：
2006-01
影响因子：
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通讯作者：
Naoya Okamoto;N. Miura;T. Seo
中科院分区：
文献类型：
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作者：
Naoya Okamoto;N. Miura;T. Seo
本文讨论了剖面分析中检验统计量分布的上界。这些检验统计量是正态总体中的Hotelling T2型统计量，其上界由F分布的上界表示。然而，在椭圆种群中，很难准确地表达它们。然后用摄动方法导出了检验统计量分布的渐近展开式，并得到了检验统计量分布的近似上界。讨论了非正态性对近似的影响，并通过Monte Carlo模拟研究评估了近似精度。
SYNOPTIC ABSTRACT The upper percentiles for the distributions of the test statistics in profile analysis are discussed. These test statistics are Hotelling's T2-type statistic in normal populations and their upper percentiles are expressed by that of the F-distributions. In elliptical populations, however, it is difficult to express them exactly. Then asymptotic expansions for the distributions of the test statistics are derived by the perturbation method and we obtain approximate upper percentiles for the distributions of the test statistics. The effect of nonnormality on approximations is discussed and the approximate accuracy is evaluated via a Monte Carlo simulation study.