## Optimal asymptotic properties of maximum likelihood estimators of parameters of some econometric modelsFour 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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0_ and covariance absolute value apply theorems argument assumed Assumption 2 implies assumptions of theorems asymptotically efficient asymptotically normally distributed autoregressive process compact set computed conditions of theorems consistent and asymptotically continuous function converges stochastically converges to zero converges uniformly defined denote distributed independently elements error terms error variables exists exogenous variables expectation and variance expected value goes to zero identically distributed independently distributed joint density lagged dependent variables Lemma linear model log likelihood function Lxl vector mean 0_ mode1 models with lagged MP sense multivariate normal nonlinear models nonsingular covariance matrix nonsingular matrix normal with mean null sequences Optimality Results positive definite Probit Model second partial derivatives second term stability condition stationary process subsystem summand t=l s=l theorems 1.1 third term uniform convergence unknown parameters upper bound variables are nonrandom Weiss's zero as required zero uniformly