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The effects of nonnormality on asymptotic distributions of some likelihood ratio criteria for testing covariance structures under normal assumption

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  • Yanagihara, Hirokazu
  • Tonda, Tetsuji
  • Matsumoto, Chieko

Abstract

This paper examines asymptotic distributions of the likelihood ratio criteria, which are proposed under normality, for several hypotheses on covariance matrices when the true distribution of a population is a certain nonnormal distribution. It is well known that asymptotic distributions of test statistics depend on the fourth moments of the true population's distribution. We study the effects of nonnormality on the asymptotic distributions of the null and nonnull distributions of likelihood ratio criteria for covariance structures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:2:p:237-264
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    References listed on IDEAS

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    1. Kano, Yutaka, 1992. "Robust statistics for test-of-independence and related structural models," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 21-26, September.
    2. A. Swain, 1975. "A class of factor analysis estimation procedures with common asymptotic sampling properties," Psychometrika, Springer;The Psychometric Society, vol. 40(3), pages 315-335, September.
    3. 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.
    4. Nagao, Hisao & Srivastava, M. S., 1992. "On the distributions of some test criteria for a covariance matrix under local alternatives and bootstrap approximations," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 331-350, November.
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    Cited by:

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    2. Marc Hallin & Davy Paindaveine & Thomas Verdebout, 2009. "Optimal rank-based testing for principal component," Working Papers ECARES 2009_013, ULB -- Universite Libre de Bruxelles.
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    4. Loperfido, Nicola, 2020. "Some remarks on Koziol’s kurtosis," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    5. Javed, Farrukh & Loperfido, Nicola & Mazur, Stepan, 2020. "Edgeworth Expansions for Multivariate Random Sums," Working Papers 2020:9, Örebro University, School of Business.
    6. Nicola Loperfido, 2023. "Kurtosis removal for data pre-processing," 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. 17(1), pages 239-267, March.
    7. 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.
    8. Hallin, Marc & Paindaveine, Davy, 2009. "Optimal tests for homogeneity of covariance, scale, and shape," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 422-444, March.
    9. Marc Hallin, 2008. "On the Non Gaussian Asymptotics of the Likelihood Ratio Test Statistic for Homogeneity of Covariance," Working Papers ECARES 2008_039, ULB -- Universite Libre de Bruxelles.

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