非正则位置参数模型中的拟极大似然估计

当分布密度的形式未知时，参数的极大似然估计没有明确的解析表达式，也不能通过设计算法由计算机运算得到。本文我们将从该分布中抽取的样本当作是来自另一个形式已知的分布密度的样本，该已知分布密度的选取依赖于未知的分布密度，但是具有与未知分布相似的边界性质。基于这两个分布族，我们提出了拟极大似然估计的概念，同时，对这种拟极大似然估计的渐近性质进行了讨论。结果表明拟极大拟然估计与极大似然估计有关相同的渐近性质，并且由于拟极大似然估计的获得不依赖于未知分布密度的形式，只与一已知的分布密度有关，使得通过计算机可以实现对其的求解。

QUASI-MAXIMUM LIKELIHOOD ESTIMATOR IN ON-REGULAR LOCATION PARAMETER MODELS

When the form of the density function is unknown, it is impossible to get the explicit expression of the MLE of the parameter. In this paper,we discuss the MLE of the location parameter in the non-regular location parameter modles. When the form of the distribution is unknown, we take samples from the unknown distribution family as the one from the other distribution family which form is known which has the similar properties as the unkown distribution family. Based on the two distribution families, we proposed the concept of quasi-MLE, meanwhile,the adaptive property of this estimate is also investigated. Because the quasi-MLE can be obtained from the known distribution family so we can edit some program and get the MLE by computer.