TESTS OF DIMENSIONALITY FOR MANOVA UNDER MULTIVARIATE t POPULATIONS

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  • Yoshida Kiyotaka
    Division of Systems and Information Engineering, Graduate School of Engineering, Hokkaido University
  • Imai Hideyuki
    Division of Systems and Information Engineering, Graduate School of Engineering, Hokkaido University
  • Sato Yoshiharu
    Division of Systems and Information Engineering, Graduate School of Engineering, Hokkaido University

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  • 多変量t母集団におけるMANOVAの次元検定について
  • タヘンリョウ t ボシュウダン ニ オケル MANOVA ノ ジゲン ケンテイ ニ ツイテ

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For tests of dimensionality in multivariate analysis of variance (MANOVA), three types of test criteria (Likelihood-Ratio-type, Lawley-Hotelling-type and Bartlett-Nanda-Pillai-type) are popular. However, as is well known, these criteria depend on nuisance parameters. Yoshida et al. (2002) suggested new criteria, which are upper bound for null distribution of the above-mentionted three types criteria and do not depend on the nuisance parameters under elliptical populations. Furthermore, it was proved that the upper bounds are upper limits for null distributions of LR-type and LH-type. In this paper, we consider tests of dimensionality under multivariate t populations, and show that the upper bounds are also upper limits for null distributions of LR-type and LH-type.

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