不同损失函数下分布族参数的极小极大估计

Minimax estimation of parameter for a class of scale distributions under different loss functions

针对一类尺度分布族参数的估计问题,在参数的先验分布为均匀分布、而损失函数为加权平方损失、MLINEX损失和对称熵损失函数下,研究了该分布族参数的Bayes估计和Minimax估计问题.最后,通过Monte Carlo数值模拟,通过计算各估计的均方误差,给出了几种估计的比较结果.

The Bayesian and Minimax estimators of unknown parameter of a class of scale distributions with uniform prior distribution were obtained under three different losses： weighted square error loss, modified linear exponential loss（MLINEX） and symmetric entropy loss function. Finally, by Monte Carlo numerical simulation and calculating the estimator of the mean square error, a numerical compare example was given to illustrate the results.