Asymptotic expansions in mean and covariance structure analysis

Haruhiko Ogasawara

Journal of Multivariate Analysis, 2009, vol. 100, issue 5, 902-912

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.

Keywords: primary; 62E20 secondary; 62H25 Mean and covariance structure Factor means Edgeworth expansion Cornish-Fisher expansion Bias Skewness Kurtosis (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (5)

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