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Testing linear hypotheses of mean vectors for high-dimension data with unequal covariance matrices
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2013 (English)In: Journal of Statistical Planning and Inference, ISSN 0378-3758, Vol. 143, no 11, 1898-1911 p.Article in journal (Refereed) Published
Abstract [en]

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. p/N -> c < infinity. 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.

Place, publisher, year, edition, pages
2013. Vol. 143, no 11, 1898-1911 p.
Keyword [en]
Cornish-Fisher transform, Dempster trace criterion, High dimensionality, Multivariate Behrens-Fisher problem, (N, p)-asymptotics
National Category
URN: urn:nbn:se:kth:diva-131703DOI: 10.1016/j.jspi.2013.07.008ISI: 000324790500009ScopusID: 2-s2.0-84883279740OAI: diva2:657249
Swedish Research Council, 421-2008-1966, 23500360

QC 20131018

Available from: 2013-10-18 Created: 2013-10-17 Last updated: 2013-10-18Bibliographically approved

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Pavlenko, Tatjana
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