Some Properties Of The Pivotal Statistic Basedon The Asymptotically Distribution-free Theory in Structural Equation Modeling

摘要

For normally distributed data, the asymptotic bias and skewness of the pivotal statistic Studentized by the asymptotically distribution-free standard error are shown to be the same as those given by the normal theory in structural equation modeling. This gives the same asymptotic null distributions of the two pivotal statistics up to the next order beyond the usual normal approximation under normality. With an alternative hypothesis, the asymptotic variances of the two statistics under normalityon normality are also derived. It is, however, shown that the asymptotic variances of the non null distributions of the statistics are generally different even under normality.