Unbiasedness as the Dual of Being Bayes
无偏性作为贝叶斯性的对偶
In this note we define the notion of unbiasedness for a decision function for an arbitrary loss function. This is a generalization of Lehmann's (1951) definition. We show that this notion of unbiasedness is a dual to the notion of being Bayes; that is, if the role of the random variable and the parameter is interchanged, then unbiasedness is equivalent to being Bayes and vice versa. Some consequences of this fact are discussed.