Econometricians have usefully separated study of estimation into identification and statistical components. Identification analysis aims to place an informative upper bound on what may be learned about population parameters of interest with specified sample data. Statistical decision theory has studied decision making with sample data without reference to identification. This paper asks if and how identification analysis is useful to statistical decision theory. I show that the answer is positive and simple when the relevant parameter (true state of nature) is point identified. However, a subtlety arises when the true state is partially identified, and a decision must be made under ambiguity. Then the performance of some criteria, particularly minimax regret, is enhanced by permitting randomized choice of an action, which essentially requires availability of sample data. I show that an informative upper bound on the performance of decision making holds when the knowledge assumed in identification analysis is combined with sample data enabling randomized choice. I emphasize that using sample data to randomize choice is conceptually distinct from its traditional econometric use to infer population parameters.
翻译:鉴定分析旨在对特定抽样数据中感兴趣的人口参数的可知性设定一个内容翔实的上限; 统计决策理论研究抽样数据的决策,而没有参考识别; 本文询问身份分析是否以及如何对统计决策理论有用; 我表明,当相关参数(自然的本质状态)被点点确定时,答案是肯定的和简单的; 但是,当真实状态被部分确定,决定必须在模糊度下作出时,就会出现一种微妙的情况。 然后,允许随机选择一项行动,特别是最微小的遗憾,从而增强某些标准的性能,这基本上需要提供抽样数据。 我表明,当身份分析中假定的知识与能够随机选择的抽样数据相结合时,决策业绩的知情性上限与抽样数据是相同的。 我强调,使用抽样数据随机选择在概念上不同于其传统的计量经济学使用来推断人口参数。