Pseudo Maximum Likelihood Methods: Theory
研究当真实概率密度函数不属于所选似然函数族时，通过最大化似然函数得到的估计量。证明了其一阶矩参数估计一致性的充要条件，以及渐近正态性和渐近协方差矩阵下界的存在性。
Estimators obtained by maximizing a likelihood function are studied in the case where the true p.d.f. does not necessarily belong to the family chosen for the likelihood function. When such a procedure is applied to the estimation of the parameters of the first order moments, it is possible to prove a necessary and sufficient condition for its consistency. Asymptotic normality is shown as well as the existence of a lower bound for the asymptotic covariance matrix. It is also seen that this bound can be reached if consistent estimates are available for the parameters of the second order moments. Finally, a necessary and sufficient condition for the consistency if the pseudo maximum likelihood estimation of the first and second moments is given.