Hiroshima Mathematical Journal

Asymptotic expansions of the distributions of MANOVA test statistics when the dimension is large

Hirofumi Wakaki, Yasunori Fujikoshi, and Vladimir V. Ulyanov

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Abstract

Asymptotic expansions of the null distribution of the MANOVA test statistics including the likelihood ratio, Lawley-Hotelling and Bartlett-Nanda-Pillai tests are obtained when both the sample size and the dimension tend to infinity with assuming the ratio of the dimension and the sample size tends to a positive constant smaller than one. Cornish-Fisher expansions of the upper percent points are also obtained. In order to study the accuracy of the approximation formulas, some numerical experiments are done, with comparing to the classical expansions when only the sample size tends to infinity.

Article information

Source
Hiroshima Math. J., Volume 44, Number 3 (2014), 247-259.

Dates
First available in Project Euclid: 26 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1419619745

Digital Object Identifier
doi:10.32917/hmj/1419619745

Mathematical Reviews number (MathSciNet)
MR3296074

Zentralblatt MATH identifier
1308.62114

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 62E20: Asymptotic distribution theory

Keywords
MANOVA high dimension likelihood ratio Lawley-Hotelling Bartlett-Nanda-Pillai Edgeworth expansion

Citation

Wakaki, Hirofumi; Fujikoshi, Yasunori; Ulyanov, Vladimir V. Asymptotic expansions of the distributions of MANOVA test statistics when the dimension is large. Hiroshima Math. J. 44 (2014), no. 3, 247--259. doi:10.32917/hmj/1419619745. https://projecteuclid.org/euclid.hmj/1419619745


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