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Asymptotic expansions in mean and covariance structure analysis

  • Ogasawara, Haruhiko
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    Asymptotic expansions of the distributions of parameter estimators in mean and covariance structures are derived. The parameters may be common to, or specific in means and covariances of observable variables. The means are possibly structured by the common/specific parameters. First, the distributions of the parameter estimators standardized by the population asymptotic standard errors are expanded using the single- and the two-term Edgeworth expansions. In practice, the pivotal statistic or the Studentized estimator with the asymptotically distribution-free standard error is of interest. An asymptotic distribution of the pivotal statistic is also derived by the Cornish-Fisher expansion. Simulations are performed for a factor analysis model with nonzero factor means to see the accuracy of the asymptotic expansions in finite samples.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00188-7
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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 5 (May)
    Pages: 902-912

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:902-912
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    1. 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.
    2. Ke-Hai Yuan & Peter Bentler, 2006. "Mean Comparison: Manifest Variable Versus Latent Variable," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 139-159, March.
    3. Haruhiko Ogasawara, 2004. "Asymptotic biases in exploratory factor analysis and structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 235-256, June.
    4. Ogasawara, Haruhiko, 2007. "Higher-order Estimation Error in Structural Equation Modeling," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 57(4), pages 131-160.
    5. Haruhiko Ogasawara, 2001. "Standard errors of fit indices using residuals in structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 421-436, September.
    6. Boik, Robert J., 2008. "An implicit function approach to constrained optimization with applications to asymptotic expansions," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 465-489, March.
    7. Ogasawara, Haruhiko, 2008. "Errata and supplement to the paper "Higher-order asymptotic cumulants of Studentized estimators in covariance structures"," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 59(2/3), pages 95-107.
    8. Yiu-Fai Yung & Peter M. Bentler, 1999. "On Added Information for ML Factor Analysis with Mean and Covariance Structures," Journal of Educational and Behavioral Statistics, American Educational Research Association, vol. 24(1), pages 1-20, March.
    9. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    10. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.
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