Imposed quasi-normality in covariance structure analysis

In the analysis of covariance structures, the distance between an observed covariance matrix S of order k x k and C(6) E(S) is minimized by searching over the 8-space. The criterion leading to a best asymptotically normal (BAN) estimator of 0 is found by minimizing the difference between vecS and vecC(6) in a metric that is based on the variance of s. So optimality requires inversion of a k2 x k2 matrix, which is a formidable task when the model contains many equations and the matrix to be inverted is structured insufficiently. The latter can happen when the underlying distribution is non-normal. We present two computationally attractive alternatives that result in estimators for 0 which are approximately BAN. Also, we compare the performance of various weight matrices by means of a Monte-Carlo simulation.