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Asymptotic expansions in mean and covariance structure analysis

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  • Ogasawara, Haruhiko
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    Abstract

    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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    Bibliographic Info

    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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    Related research

    Keywords: primary; 62E20 secondary; 62H25 Mean and covariance structure Factor means Edgeworth expansion Cornish-Fisher expansion Bias Skewness Kurtosis;

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    Cited by:
    1. Shimizu, Hiroaki & Wakaki, Hirofumi, 2011. "Asymptotic expansions for a class of tests for a general covariance structure under a local alternative," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1080-1089, July.
    2. Ogasawara, Haruhiko, 2009. "Supplement to Ogasawara's papers on "the ADF pivotal statistic", "mean and covariance structure analysis", and "maximal reliability"," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 60(1), pages 21-44.
    3. Ogasawara, Haruhiko, 2012. "Cornish-Fisher expansions using sample cumulants and monotonic transformations," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 1-18, January.

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