Optimal asymptotic properties of maximum likelihood estimators of parameters of some econometric models
Four theorems are proven, which simplify the application to econometric models of Weiss's theorem on asymptotic properties of maximum likelihood estimators in nonstandard cases. The theorems require, roughly: the uniform convergence in any compact sets of the unknown parameters of the expection of the Hessian matrix of the log likelihood function; and the uniform convergence to 0 in the same sense of the variance of the same quantities. The fourth theorem allows one to conclude that the optimal properties hold on an image set of the parameters when the map satisfies certain smoothness conditions, and the first three theorems are satisfied for the original parameter set. These four theorems are applied to autoregressive models, nonlinear models, systems of equations, and probit and logit models to infer optimal asymptotic properties. (Author).
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