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-order moments is investigated. The asymptotic optimality extends to the whole vector of parameter estimators, if additional restrictions on the third-order moments of the variables are imposed. Results related to the optimality of normal (pseudo) maximum likelihood methods are also encompassed. The results derived concern a wide class of latent-variable models and estimation methods used routinely in software for the analysis of latent-variable models such as LISREL, EQS, and CALIS. The general results are specialized to the context of multivariate regression and simultaneous equations with errors in variables.
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