On the Asymptotic Behaviour of General Maximum Likelihood Estimates for the Nonregular Case Under Nonstandard Conditions
将Huber的经典结果推广到非正则情形,针对单变量模型给出了在模型邻域内渐近无偏的稳健估计量,其收敛速度与极大似然估计相同,且部分估计量在中心模型下渐近有效。
In this paper we generalize Huber's (1967) results to include the nonregular case. Resistant estimators which turn out to be asymptotically unbiased in a neighbourhood of the model are given for some univariate models. Their order of consistency achieves the rate of the maximum likelihood estimates. Moreover, some of the estimates are asymptotically efficient under the central model, in the sense that they have the same asymptotic distribution as the maximum likelihood estimate.