Testing linear hypotheses of mean vectors for high-dimension data with unequal covariance matrices

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• 作者：Takahiro Nishiyama ; Masashi Hyodo ; Takashi Seo ; Tatjana Pavlenko
• 关键词：Cornish&ndash ; Fisher transform ; Dempster trace criterion ; High dimensionality ; Multivariate Behrens&ndash ; Fisher problem ; (N ; p)-asymptotics
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2013
• 出版时间：November, 2013
• 年：2013
• 卷：143
• 期：11
• 页码：1898-1911
• 全文大小：298 K

文摘

We propose a new test procedure for testing linear hypothesis on the mean vectors of normal populations with unequal covariance matrices when the dimensionality, p exceeds the sample size N, i.e. . Our procedure is based on the Dempster trace criterion and is shown to be consistent in high dimensions.

The asymptotic null and non-null distributions of the proposed test statistic are established in the high dimensional setting and improved estimator of the critical point of the test is derived using Cornish-Fisher expansion. As a special case, our testing procedure is applied to multivariate Behrens-Fisher problem. We illustrate the relevance and benefits of the proposed approach via Monte-Carlo simulations which show that our new test is comparable to, and in many cases is more powerful than, the tests for equality of means presented in the recent literature.