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Robust statistics for test-of-independence and related structural models

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  • Kano, Yutaka

Abstract

Recent research of asymptotic robustness shows that the likelihood ratio (LR) test statistic for test-of-independence based on normal theory remains valid for a general case where only independence is assumed. In contrast, under elliptical populations the LR statistic is correct if a kurtosis adjustment is made. Thus, the LR statistic itself is available for the first case, whereas a certain correction is needed for the second framework, which is seriously inconvenient for practitioners. In this article, we propose an alternative adjustment to the LR statistic which can be utilized for both of the distribution families. The theory is derived in the context of general linear latent variate models.

Suggested Citation

  • Kano, Yutaka, 1992. "Robust statistics for test-of-independence and related structural models," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 21-26, September.
    • Handle: RePEc:eee:stapro:v:15:y:1992:i:1:p:21-26
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    Citations

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    Cited by:

    1. 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.
    2. Ke-Hai Yuan & Peter Bentler, 2004. "On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 437-457, September.
    3. 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.
    4. Yanagihara, Hirokazu, 2007. "A family of estimators for multivariate kurtosis in a nonnormal linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 1-29, January.
    5. Yuan, Ke-Hai & Bentler, Peter M., 1999. "On asymptotic distributions of normal theory MLE in covariance structure analysis under some nonnormal distributions," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 107-113, April.
    6. Yuan, Ke-Hai & Bentler, Peter M., 2005. "Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 328-343, June.

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