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Published in:
2020 | OriginalPaper | Chapter
3. MANOVA Test Statistics
Authors : Yasunori Fujikoshi, Vladimir V. Ulyanov
Published in: Non-Asymptotic Analysis of Approximations for Multivariate Statistics
Publisher: Springer Singapore
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Abstract
The main purpose of this chapter is to give a method for obtaining error bounds for asymptotic expansions of the null distributions of Hotelling’s \(T^2\) (or Lawley–Hotelling criterion, \(T_{LH}\)), the likelihood-ratio criterion \(T_{LR}\) and the Bartlett–Nanda–Pillai criterion \(T_{BNP}\) in the MANOVA model when the sample size is large. The results for \(T_{LH}\) and \(T_{LR}\) are obtained by expressing these statistics in terms of a multivariate scale mixture, and using error bounds evaluated in \(L_1\)-norm. The error bound is given for the limiting distribution of \(T_{BNP}\) by using a relationship between \(T_{BNP}\) and \(T_{LH}\). Further, we give error bounds for these criteria when the sample size and the dimension are large.