极大似然估计不变性的拓展

Extention of the invariance of maximum likelihood estimation

某一参数估计是否是"最优"估计,通常要从一致性、无偏性、有效性、不变性等方面进行讨论,进而通过实际的观察对其进行数据拟合,分析其相对于实际模型的偏差程度。针对参数估计评选标准中的不变性进行了进一步的探讨。根据参数极大似然估计不变性原则,给出在一定条件下极大似然估计具有不变性的充分必要条件,并利用该结论计算了二元正态分布Z=(X,Y)的未知参数σ2和ρ的极大似然估计值。

For some parametric estimation, whether it is the best estimation or not, its consistency, unbiasedness, effectiveness, invariance, and so on are often discussed. Then, it is compared with the data we get from experiment, and the deviation with the experimental data is considered. The invariance of estimator deeply discussed. Based on the invariance of maximum likelihood estimation, the sufficient and necessary condition under which the maximum likelihood estimation has invariance for the parameters are given, then it uses this conclusion to calculate the maximum likelihood estimation of σ^2 and ρ for bivariate normal distribution.