论文标题
身份和统计决策理论
Identification and Statistical Decision Theory
论文作者
论文摘要
计量经济学家已经有效地将估计的研究分为识别和统计组成部分。识别分析假设了解可观察到的数据的概率分布的知识,它可以通过有限的样本数据了解有关感兴趣的人群参数的上限。然而,瓦尔德(Wald)的统计决策理论研究决策与样本数据的决策无参考,实际上没有参考估计。本文询问识别分析是否对统计决策理论有用。答案是积极的,因为它可以在决策标准的有限样本性能上产生信息丰富且可牵引的上限。当确定与决策相关参数点时,推理很简单。当真正确定真正的状态并且必须在歧义下做出决定时,它会更加精致。然后,通过随机选择动作,可以增强某些标准的性能,例如minimax遗憾。这可以通过使选择成为样本数据的函数来实现。我发现,重铸造统计决策功能作为选择集合元素的选择概率的选择是有用的。使用示例数据从概念上随机化选择与其传统用途以估算人口参数的概念不同,并且是互补的。
Econometricians have usefully separated study of estimation into identification and statistical components. Identification analysis, which assumes knowledge of the probability distribution generating observable data, places an upper bound on what may be learned about population parameters of interest with finite sample data. Yet Wald's statistical decision theory studies decision making with sample data without reference to identification, indeed without reference to estimation. This paper asks if identification analysis is useful to statistical decision theory. The answer is positive, as it can yield an informative and tractable upper bound on the achievable finite sample performance of decision criteria. The reasoning is simple when the decision relevant parameter is point identified. It is more delicate when the true state is partially identified and a decision must be made under ambiguity. Then the performance of some criteria, such as minimax regret, is enhanced by randomizing choice of an action. This may be accomplished by making choice a function of sample data. I find it useful to recast choice of a statistical decision function as selection of choice probabilities for the elements of the choice set. Using sample data to randomize choice conceptually differs from and is complementary to its traditional use to estimate population parameters.