Bayes Convolution
在贝叶斯框架下提出一个通用卷积定理，证明在正态、对数伽马和指数位置模型中存在最优估计量，并指出正态和对数伽马是仅有的光滑位置情形。
Summary A general convolution theorem within a Bayesian framework is presented. Consider estimation of the Euclidean parameter θ by an estimator T within a parametric model. Let W be a prior distribution for θ and define G as the W ‐average of the distribution of T ‐ θ under θ . In some cases, for any estimator T the distribution G can be written as a convolution G = K * L with K a distribution depending only on the model, i.e. on W and the distributions under θ of the observations. In such a Bayes convolution result optimal estimators exist, satisfying G = K . For location models we show that finite sample Bayes convolution results hold in the normal, loggamma and exponential case. Under regularity conditions we prove that normal and loggamma are the only smooth location cases. We also discuss relations with classical convolution theorems.