平方损失下区间有界的尺度函数极小极大估计

Minimax estimation in scale parameter families as the parameter interval being bounded under squared loss function

给出了尺度参数θ有界时,函数h(θ)的极小极大估计存在的充分条件,并给出了两点先验时最不利先验的充分条件,证明了关于两点最不利先验的Bayes估计就是极小极大估计.

When the scale parmeter θ lies in a bounded interval, a sufficient condition is described in the present paper,under which the minimax estimator of h（θ） exists. Sufficient conditions are derived which ensure that a two-point priori is least favorable priori. It is shown that Bayes estimator with respect to this priori is minimax estimator.