Convergence Rate of Strong Consistency of the Maximum Likelihood Estimator in Exponential Family Nonlinear Models

摘要

This article proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of the maximum likelihood estimator (MLE) in exponential family nonlinear models (EFNM) and give its convergence rate. In an important case, we obtain the convergence rate O(n~(-1/2)(log log n)~(1/2))—the rate as that in the Law of the Iterated Logarithm (LIL) for iid partial sums and thus cannot be improved anymore.