文章基本信息

标题：An adaptive spatial-sign-based test for mean vectors of elliptically distributed high-dimensional data
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作者：Zhou, Bu ; Zhou, Bu ; Guo, Jia 等
期刊名称：Statistics and Its Interface
印刷版ISSN：1938-7989
电子版ISSN：1938-7997
出版年度：2019
卷号：12
期号：1
页码：93-106
DOI：10.4310/SII.2019.v12.n1.a9
出版社：International Press
摘要：Recently, a nonparametric test for mean vectors of elliptically distributed high-dimensional data has been proposed in the literature. The asymptotic normality of the test statistic under some strong assumptions is established. In practice, however, these strong assumptions may not be satisfied or hardly be checked so that the above test may not perform well in terms of size control. In this paper, we propose an adaptive spatial-sign-based test for mean vectors of elliptically distributed high-dimensional data without imposing strong assumptions. The null distribution of the proposed test statistic is shown to be a chi-squared mixture which is generally skewed. We propose to approximate the null distribution using the well-known Welch–Satterthwaite $\chi^2$-approximation. The resulting approximate distribution is able to adapt to the shape of the underlying null distribution of the proposed test statistic. Simulation studies and three real data examples demonstrate that the proposed test has a better size control than the existing nonparametric test while both tests enjoy about the same powers..
关键词：High-dimensional data; Spatialsign-based test; Welch–Satterthwaite χ2-approximation.