Statistical Inference
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AI 根据所提供的论文材料归类：摘要讨论统计决策与推断的基础理论，未明确任何所列经济计量细分领域。
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统计推断
- 研究问题
- 当实验设计已经确定且结果已经观测，如何以统计决策规则指导未来行动，并明确所谓最佳决策还需要哪些额外规定？
- 方法与思路
- 作者在公理化概率框架下讨论实验结果分析，先说明某类决策函数的存在并构造该类，再应用于分类、估计和假设检验。
- 材料陈述的贡献
- 摘要称存在并可构造在特定意义下最优的一类决策函数，同时讨论赋予最佳决策明确含义前还必须指定的内容。
- 阅读关注点
- 应核对最优性的准确含义、决策函数类别的构造条件，以及比较决策所需的额外规定和各统计问题中的对应形式。
- 阅读边界
- 仅据 Crossref 摘要；最优性准则和所需条件未具体展开，不能将某类规则的最优性理解为存在无条件最佳统计方法。
原文摘要
Summary The subject matter of mathematical statistics may be divided into two parts, the theory of probability and the theory of inference. The first is concerned with deductions from the population to the sample; the second with inferences from the sample to the population, and may further be subdivided into the design and analysis of experiments. In the present paper we are concerned with this latter subdivision. We use the axiomatic theory of Kolmogorov as our theory of probability, and we suppose that the design of the experiment has been selected and the experiment carried out: our problem is that of analyzing the results. We suppose that the purpose of the analysis is to make decisions for future action, and that we have to choose which decision to take on the basis of the observed result of the experiment. A rule for making these decisions is called a decision function, and in §1 we show there exists a class of decision functions which is, in a sense to be explained, optimum, and in §2 we construct this class. In §3 the consequences of the previous results are discussed and we are able to appreciate what further has to be specified before a meaning can be given to the phrase “the best decision function”. In §4 these ideas are applied to some common statistical problems of classification, estimation and tests of hypotheses.