Covariance structure analysis with heterogeneous kurtosis parameters

Abstract

This paper discusses the analysis of covariance structures in a wide class of multivariate distributions whose marginal distributions may have heterogeneous kurtosis parameters. Elliptical distributions often used as a generalization of the normal theory are members of this class. It is shown that a simple adjustment of the weight matrix of normal theory, using kurtosis estimates, results in an asymptotically efficient estimator of structural parameters within the class of estimators that minimize a general discrepancy function. Results are obtained for arbitrary covariance structures as well as those that meet a scale invariance assumption. Two real data sets are analyzed for illustrative purposes.