Asymptotic distribution theory in the analysis of covariance structures
Alexander Shapiro · South African Statistical Journal · 1983
In this paper we present a unified approach to the asymptotic distribution theory of covariance structures. Our approach is based on the differential calculus of min-max functions, which is developed in the first sections of the paper. The general theory is demonstrated by means of generalized least squares estimators. New and well-known results are obtained in the general framework. In particular, the asymptotic behavior of the estimators under an alternative hypothesis and the problem of non-identifiability are discussed. Finally, potential possibilities of the theory are illustrated by the example of minimum trace factor analysis.