11 - Statistical Inference of Moment Structures

Abstract

This chapter discusses the statistical inference of moment structure models where first and second population moments are hypothesized to have a parametric structure. Classical examples of such models are multinomial and covariance structure models. Although the theory is presented in terms of general moment structures, the main emphasis is on the analysis of covariance structures. Identifiability and the minimum discrepancy function (MDF) approach to statistical analysis (estimation) of such models are also discussed in the chapter. Consistency, asymptotic normality of MDF estimators, and asymptotic chi-squaredness of MDF test statistics are addressed. Results addressing asymptotic robustness of the normal theory based MDF statistical inference in the analysis of covariance structures are also presented. The chapter also reviews the Browne–Shapiro approach, which uses a strong assumption of the existence of the fourth-order moments.