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Subject: LCSH

Distribution (Probability theory)




Based on Lauter's (Biometrics, 1996) exact t test for biometrical studies related to the multivariate normal mean, we develop a generalized F-test for the multivariate normal mean and extend it to multiple comparison. The proposed generalized F- tests have simple approximate null distributions. A Monte Carlo study and two real examples show that the generalized F-test is at least as good as the optional individual LÄauter's test and can improve its performance in some situations where the projection directions for the LÄauter's test may not be suitably chosen. It is discussed that the generalized F-test could be superior to individual Lauter's tests and the classical Hotelling T2-test for the general purpose of testing the multivariate normal mean. It is shown by Monte Carlo studies that the extended generalized F- test outperforms the commonly-used classical test for multiple comparison of normal means in the case of high dimension with small sample sizes. AMS Classification: 62F03; 62F05


NOTICE: This is the author’s version of a work that was accepted for publication in Computational Statistics & Data Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computational Statistics & Data Analysis, 53, 4, p.1177-1190. It can be accessed here.



Publisher Citation

Liang, J. & Tang, M.-L. (2009). Generalized F -tests for the multivariate normal mean. Computational Statistics & Data Analysis, 2009. 53(4): p. 1177-1190.

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