Hypothesis Testing When the Sample Size is Treated as a Random Variable
将样本量视为随机变量时的假设检验AI 解读 ↓
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将样本量视为随机变量时的假设检验
- 研究问题
- 当样本量是随机变量而非固定常数时，如何定义和构造假设检验，并在未知样本量分布下选择合适的拒绝阈值？
- 方法与思路
- 作者先分析简单原假设对简单备择的似然比检验，再讨论复合备择，并以数值计算从频率学角度比较若干候选检验。
- 材料陈述的贡献
- 摘要称，简单对简单情形的最优检验阈值不随样本量变化，并提出两种阈值确定方法；复合备择比较属于探索性分析。
- 阅读关注点
- 应核对随机样本量的生成机制、最优性采用的约束、未知样本量分布时的校准办法，以及数值比较的适用范围。
- 阅读边界
- 仅据Crossref摘要，复合备择部分提供的是探索性数值证据；不能据此认为任意停止规则下都可把样本量当作固定。
原文摘要
Summary In the Neyman-Pearson theory of hypothesis testing it is customary to calculate significance levels and power functions on the assumption that the sample size is fixed. The main purpose of this paper is to propagate the view that the restriction of the theory to reference sets in which the sample size is constant is neither necessary nor desirable. The paper falls into two parts. In the first we consider the test of a simple null hypothesis versus a simple alternative. In this case it is pointed out that the optimum test requires the rejection of the null hypothesis if the likelihood ratio is less than a constant, K, which is independent of n, the sample size. In this respect it is identical with Bayesian and likelihood methods of dealing with the same problem. Two methods for determining a suitable value for K in the absence of knowledge about the distribution of sample size are proposed. These ideas are extended, in the second part of the paper, to the case of a simple null hypothesis and a composite alternative. Since no uniformly most powerful test exists, a variety of tests suggested by Bayesian and likelihood considerations are compared from a frequentist point of view. This work is exploratory, being based on numerical calculations, but provides a partial justification for treating sample size as if it were fixed.