统计决策的统计推断

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摘要翻译：
统计决策理论的Wald发展解决了用样本数据进行决策的问题。Wald的统计决策函数(SDF)的概念包含了[data->decision]形式的所有映射。SDF不需要执行统计推断；也就是说，它不需要使用数据来得出关于自然真实状态的结论。基于推理的SDF具有顺序形式[数据->推理->决策]。本文将基于推理的SDFs作为决策的实用程序，可以实现Wald的一些设想。本文首先讨论二元选择问题，其中所有的SDF都可以看作是假设检验。接下来，它考虑Ias if优化，它使用真实状态的点估计，好像估计是准确的。然后，它将这一思想扩展到假设最大化决策和极小极大后悔决策，这两种决策使用真实状态的某些特征的点估计，就好像它们是准确的一样。本文主要采用有限样本最大遗憾来评价基于推理的SDFS的性能。为了说明抽象的想法，它提出了关于治疗选择和点预测与样本数据的具体发现。
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英文标题：
《Statistical inference for statistical decisions》
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作者：
Charles F. Manski
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最新提交年份：
2019
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data -> decision]. An SDF need not perform statistical inference; that is, it need not use data to draw conclusions about the true state of nature. Inference-based SDFs have the sequential form [data -> inference -> decision]. This paper motivates inference-based SDFs as practical procedures for decision making that may accomplish some of what Wald envisioned. The paper first addresses binary choice problems, where all SDFs may be viewed as hypothesis tests. It next considers as-if optimization, which uses a point estimate of the true state as if the estimate were accurate. It then extends this idea to as-if maximin and minimax-regret decisions, which use point estimates of some features of the true state as if they were accurate. The paper primarily uses finite-sample maximum regret to evaluate the performance of inference-based SDFs. To illustrate abstract ideas, it presents specific findings concerning treatment choice and point prediction with sample data.
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PDF链接：
https://arxiv.org/pdf/1909.06853

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关键词：统计推断 econometrics Multivariate Optimization Statistical 选择 决策 true 看作 sample