q对称熵损失函数下正态总体刻度参数的估计

用参数估计的方法, 研究均值为0的正态分布中刻度参数在q对称熵损失函数下的最小风险同变估计、 Bayes估计和Minimax估计, 并讨论了 ［cT+d］^1/2形式的估计量当0≤c*, d>0; c=c^*, d≥0时是可容许的, 当0*, d=0; c>c^*, d>0时是不可容许的.

Estimation of Scale Parameter of Normal Distribution under q-Symmetric Entropy Loss Function

By means of the parameter estimation, we give the Bayesian estimation, the minimum risk equivalent estimation and the minimax estimation of scale parameter σ under the q symmetric entropy loss function in the normal distribution, its mean of which is 0. Furthermore, when 0≤c*, d>0; c=c^*, d≥0, the estimator with the form of ［cT+d］^1/2 is admissible; when 0*, d=0; c>c^*, d>0, ［cT+d］^1/2 is inadmissible.