独立指数分布期望参数的Γ极小极大估计

Γ-minimax estimation for exponential distribution parameter

在参数的部分先验信息已知的条件下所获得的Γ极小极大估计是一种介于有确定的先验分布函数的Bayes估计和无先验信息的极小极大估计之间的估计方法,因而更切合实际。以往的研究对二项分布参数的线性组合及负二项分布的参数在某些限制条件下的Γ极小极大估计做了讨论。本文给出了独立指数分布的期望参数在一般的先验矩限制下的Γ极小极大估计,同时讨论了两种特殊情况,即给出了在仅有先验二阶矩限制下的以及有确定的先验一阶矩和二阶矩限制下的指数分布的期望参数的Γ极小极大估计。

Compared with the Bayesian estimation with a determined prior distribution and the Minimax estimation with zero-information prior distribution, a better one is the Γ-estimation for the parameter of a distribution when only parts of the information for its prior distribution is know. And it is more practicable. In recent study, the Γ- minimax estimation for the linear combination of parameters of binomial distributions and for the parameter of a negative binomial distribution were discussed subject to the certain restriction. As for the independent exponential distribution, the Γ- minimax estimation for the expectation are derived when the first and second rank matrix of prior distribution are restricted generally. Furthermore two special cases are studied, one is only the second rank matrix of prior distribution is restricted, and another is definite values for the first and second rank matrix of prior distribution.