IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i9p1914-1926.html
   My bibliography  Save this article

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Author

Listed:
  • Siotani, Minoru
  • Wakaki, Hirofumi

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.

Suggested Citation

  • Siotani, Minoru & Wakaki, Hirofumi, 2006. "Contributions to multivariate analysis by Professor Yasunori Fujikoshi," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1914-1926, October.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:1914-1926
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(06)00076-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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;The Institute of Statistical Mathematics, vol. 29(1), pages 379-387, December.
    4. 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;The Institute of Statistical Mathematics, vol. 27(1), pages 99-108, 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. Yasunori Fujikoshi & Chinubal Khatri, 1990. "A study of redundancy of some variables in covariate discriminant analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(4), pages 769-782, December.
    7. 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.
    8. 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.
    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. 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.
    11. Fujikoshi, Yasunori, 2000. "Transformations with Improved Chi-Squared Approximations," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 249-263, February.
    12. Fujikoshi, Yasunori & Watamori, Yoko, 1992. "Tests for the mean direction of the Langevin distribution with large concentration parameter," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 210-225, August.
    13. 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.
    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 & 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.
    16. 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.
    17. Fujikoshi, Y. & Ulyanov, V.V. & Shimizu, R., 2005. "L1-norm error bounds for asymptotic expansions of multivariate scale mixtures and their applications to Hotelling's generalized," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 1-19, September.
    18. 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.
    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;The Institute of Statistical Mathematics, 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.
    21. Fujisawa, Hironori, 1997. "Improvement on Chi-Squared Approximation by Monotone Transformation," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 84-89, January.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ke-Hai Yuan & Yubin Tian & Hirokazu Yanagihara, 2015. "Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 379-405, June.
    2. Xu, Jin & Gupta, Arjun K., 2006. "Improved confidence regions for a mean vector under general conditions," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1051-1062, November.
    3. Fujikoshi, Yasunori & Enomoto, Rie & Sakurai, Tetsuro, 2013. "High-dimensional AIC in the growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 239-250.
    4. Yanagihara, Hirokazu & Tonda, Tetsuji & Matsumoto, Chieko, 2005. "The effects of nonnormality on asymptotic distributions of some likelihood ratio criteria for testing covariance structures under normal assumption," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 237-264, October.
    5. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On Finite Sample Properties of Alternative Estimators of Coefficients in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-577, CIRJE, Faculty of Economics, University of Tokyo.
    6. Petzold, Max & Jonsson, Robert, 2003. "Maximum Likelihood Ratio based small-sample tests for random coefficients in linear regression," Working Papers in Economics 102, University of Gothenburg, Department of Economics.
    7. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Estudillo-Martínez, M.D., 2014. "Burbea–Rao divergence based statistics for testing uniform association," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 1-18.
    8. Alban Mbina Mbina & Guy Martial Nkiet & Fulgence Eyi Obiang, 2019. "Variable selection in discriminant analysis for mixed continuous-binary variables and several groups," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 773-795, September.
    9. Sadanori Konishi, 1977. "Asymptotic expansion for the distribution of a function of latent roots of the covariance matrix," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 389-396, December.
    10. Ohlson, Martin & von Rosen, Dietrich, 2010. "Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1284-1295, May.
    11. Nkiet, Guy Martial, 2012. "Direct variable selection for discrimination among several groups," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 151-163.
    12. Taneichi, Nobuhiro & Sekiya, Yuri & Toyama, Jun, 2011. "Improved transformed deviance statistic for testing a logistic regression model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1263-1279, October.
    13. Watanabe, Daisuke & Okada, Susumu & Fujikoshi, Yasunori & Sugiyama, Takakazu, 2008. "Large sample approximations for the LR statistic for equality of the smallest eigenvalues of a covariance matrix under elliptical population," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2714-2724, January.
    14. Ploeg, Jan van der & Bekker, Paul A., 1995. "Efficiency bounds for instrumental variable estimators under group-asymptotics," Research Report 95B24, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    15. Fujikoshi, Yasunori & Ulyanov, Vladimir V., 2006. "Error bounds for asymptotic expansions of Wilks' lambda distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1941-1957, October.
    16. Calinski, Tadeusz & Lejeune, Michel, 1998. "Dimensionality in Manova Tested by a Closed Testing Procedure," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 181-194, May.
    17. Forchini, Giovanni, 2010. "The Asymptotic Distribution Of The Liml Estimator In A Partially Identified Structural Equation," Econometric Theory, Cambridge University Press, vol. 26(3), pages 917-930, June.
    18. Soler, Julia M. P. & Singer, Julio M., 2000. "Optimal covariance adjustment in growth curve models," Computational Statistics & Data Analysis, Elsevier, vol. 33(1), pages 101-110, March.
    19. Yuan, Ke-Hai & Hayashi, Kentaro & Bentler, Peter M., 2007. "Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1262-1282, July.
    20. Yukitoshi Matsushita & Taisuke Otsu, 2020. "Second-order refinements for t-ratios with many instruments," STICERD - Econometrics Paper Series 612, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:1914-1926. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.