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Contributions to multivariate analysis by Professor Yasunori Fujikoshi

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  • Siotani, Minoru
  • Wakaki, Hirofumi
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    Abstract

    The purpose of this article is to review the findings of Professor Fujikoshi which are primarily in multivariate analysis. He derived many asymptotic expansions for multivariate statistics which include MANOVA tests, dimensionality tests and latent roots under normality and nonnormality. He has made a large contribution in the study on theoretical accuracy for asymptotic expansions by deriving explicit error bounds. A large contribution has been also made in an important problem involving the selection of variables with introducing "no additional information hypotheses" in some multivariate models and the application of model selection criteria. Recently he is challenging to a high-dimensional statistical problem. He has been involved in other topics in multivariate analysis, such as power comparison of a class of tests, monotone transformations with improved approximations, etc.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 9 (October)
    Pages: 1914-1926

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:1914-1926

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    Related research

    Keywords: Asymptotic expansions MANOVA Dimensionality Latent roots Growth curve model Selection of variables Error bounds Monotone transformations;

    References

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    1. Y. Fujikoshi, 1977. "An asymptotic expansion for the distributions of the latent roots of the Wishart matrix with multiple population roots," Annals of the Institute of Statistical Mathematics, Springer, vol. 29(1), pages 379-387, December.
    2. Fujikoshi, Y., 1978. "Asymptotic expansions for the distributions of some functions of the latent roots of matrices in three situations," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 63-72, March.
    3. Kariya, T. & Fujikoshi, Y. & Krishnaiah, P. R., 1987. "On tests for selection of variables and independence under multivariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 21(2), pages 207-237, April.
    4. Yasunori Fujikoshi & Chinubal Khatri, 1990. "A study of redundancy of some variables in covariate discriminant analysis," Annals of the Institute of Statistical Mathematics, Springer, vol. 42(4), pages 769-782, December.
    5. Fujikoshi, Yasunori, 1974. "The likelihood ratio tests for the dimensionality of regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 327-340, September.
    6. Fujikoshi, Yasunori & von Rosen, Dietrich, 2000. "LR Tests for Random-Coefficient Covariance Structures in an Extended Growth Curve Model," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 245-268, November.
    7. Fujikoshi, Yasunori & Shimizu, Ryoichi, 1989. "Error bounds for asymptotic expansions of scale mixtures of univariate and multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 279-291, August.
    8. Fujikoshi, Yasunori, 1985. "Selection of variables in two-group discriminant analysis by error rate and Akaike's information criteria," Journal of Multivariate Analysis, Elsevier, vol. 17(1), pages 27-37, August.
    9. Fujikoshi, Yasunori, 1988. "Comparison of powers of a class of tests for multivariate linear hypothesis and independence," Journal of Multivariate Analysis, Elsevier, vol. 26(1), pages 48-58, July.
    10. Gupta, A. K. & Sheena, Y. & Fujikoshi, Y., 2005. "Estimation of the eigenvalues of noncentrality parameter matrix in noncentral Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 1-20, March.
    11. Fujikoshi, Yasunori & Isogai, Takafumi, 1976. "Lower bounds for the distributions of certain multivariate test statistics," Journal of Multivariate Analysis, Elsevier, vol. 6(2), pages 250-255, June.
    12. Fujikoshi, Yasunori & Morimune, Kimio & Kunitomo, Naoto & Taniguchi, Masanobu, 1982. "Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system," Journal of Econometrics, Elsevier, vol. 18(2), pages 191-205, February.
    13. Fujisawa, Hironori, 1997. "Improvement on Chi-Squared Approximation by Monotone Transformation," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 84-89, January.
    14. Gupta, Arjun K. & Xu, Jin & Fujikoshi, Yasunori, 2006. "An asymptotic expansion of the distribution of Rao's U-statistic under a general condition," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 492-513, February.
    15. Fujikoshi, Yasunori, 2000. "Transformations with Improved Chi-Squared Approximations," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 249-263, February.
    16. Yasunori Fujikoshi, 1975. "Asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis," Annals of the Institute of Statistical Mathematics, Springer, vol. 27(1), pages 99-108, December.
    17. Fujikoshi, Y., 1977. "Asymptotic expansions of the distributions of the latent roots in MANOVA and the canonical correlations," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 386-396, September.
    18. Wakaki, Hirofumi & Eguchi, Shinto & Fujikoshi, Yasunori, 1990. "A class of tests for a general covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 313-325, February.
    19. Y. Fujikoshi & T. Kanda & N. Tanimura, 1990. "The growth curve model with an autoregressive covariance structure," Annals of the Institute of Statistical Mathematics, Springer, vol. 42(3), pages 533-542, September.
    20. Satoh, Kenichi & Kobayashi, Mika & Fujikoshi, Yasunori, 1997. "Variable Selection for the Growth Curve Model," Journal of Multivariate Analysis, Elsevier, vol. 60(2), pages 277-292, February.
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