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On asymptotic distributions of normal theory MLE in covariance structure analysis under some nonnormal distributions

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  • Yuan, Ke-Hai
  • Bentler, Peter M.

Abstract

Within some classes of nonnormal distributions, we study the asymptotic distribution of the MLE in a covariance structure model based on an incorrect assumption of normality. The asymptotic covariance matrix of the MLE has a similar form as found when the sampling distribution is elliptical, though the true sampling distribution can have arbitrary marginal skewnesses and kurtoses. The asymptotic covariance of some subset of the parameter estimators can be obtained by rescaling its normal theory counterpart. Specific models are considered as examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:2:p:107-113
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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.
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    Cited by:

    1. Nagahara, Yuichi, 2004. "A method of simulating multivariate nonnormal distributions by the Pearson distribution system and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 1-29, August.
    2. Zheng, Bang Quan, 2021. "RGLS and RLS in Covariance Structure Analysis," SocArXiv aejgf, Center for Open Science.
    3. Ke-Hai Yuan & Peter M. Bentler & Wei Zhang, 2005. "The Effect of Skewness and Kurtosis on Mean and Covariance Structure Analysis," Sociological Methods & Research, , vol. 34(2), pages 240-258, November.
    4. Wong, M. Y. & Cox, D. R., 2001. "A Test of Multivariate Independence Based on a Single Factor Model," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 219-225, November.
    5. Yuan, Ke-Hai & Bentler, Peter M., 2000. "Inferences on Correlation Coefficients in Some Classes of Nonnormal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 230-248, February.
    6. Ke-Hai Yuan & Ying Cheng & Wei Zhang, 2010. "Determinants of Standard Errors of MLEs in Confirmatory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 633-648, December.
    7. Yuan, Ke-Hai & Bentler, Peter M., 2006. "Asymptotic robustness of standard errors in multilevel structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1121-1141, May.

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