柯西分布族对数似然方程根的大样本性质

Large Sample Size Property of the Root of Log Likelihood Equation for Cauchy Distribution

文章针对一类具体的分布族———柯西分布族中参数θ,证明了存在θ的一个强相合且最好渐近正态估计^θ,它以概率1当样本量n充分大时是对数似然方程的根。

For the parameter θ in Cauchy distribution, we prove that there exists a strongly consistent and asymptoticly normal estimator θn, which, in probability 1, is the root of the log-likelihood equation when the sample size n is sufficiently large.