ON THE ASYMPTOTIC OPTIMALITY OF ALTERNATIVE MINIMUM-DISTANCE ESTIMATORS IN LINEAR LATENT-VARIABLE MODELS

In the context of linear latent-variable models, and a general type of distribution of the data, the asymptotic optimality of a subvector of minimum-distance estimators whose weight matrix uses only second-orde r moments is investigated. The asymptotic optimality extends to the wh ole vector of parameter estimators, if additional restrictions on the third-order moments of the variables are imposed. Results related to t he optimality of normal (pseudo) maximum likelihood methods are also e ncompassed. The results derived concern a wide class of latent-variabl e models and estimation methods used routinely in software for the ana lysis of latent-variable models such as LISREL, EQS, and CALIS. The ge neral results are specialized to the context of multivariate regressio n and simultaneous equations with errors in variables.