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

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.