凸函数的某些性质及其在凸损失下Bayes估计中的应用

ON SOME PROPERTIES OF CONVEX FUNCTIONS AND THEIR APPLICATIONS IN BAYES ESTIMATION WITH THE CONVEX LOSS

本文从微分的角度给出了凸函数的充要条件及其某些性质.据此我们推广了1963年Degroot和Rao在凸损失下的Bayes估计的主要结果.

In this paper, we first discuss some properties of convex functions, and then we apply these results to improve DeGroot and Rao's main theory about Bayes estimation with the convex loss in 1963.