论文标题
褪色边界：在Kiefer的非参数变体上 - Weiss问题
Fading Boundaries: On a Nonparametric Variant of the Kiefer--Weiss Problem
论文作者
论文摘要
提出和调查了Kiefer的非参数变体。类似于经典的Kiefer- Weiss问题，目的是最大程度地减少顺序测试的最大预期样本量。但是，它没有在给定样品空间上定义的所有分布上取出最大的参数分布家族。陈述了两个最佳条件，一个必要的和一个足够的条件。后者基于对顺序检测中更通用的最小值问题的现有结果。这些结果是专业化的，并在本文中明确。结果表明，非参数kiefer-Weiss测试与其参数对应物明显不同，并且可以说是非标准的，可以说是违反直觉的属性。特别是，它可以不截断，并且严格取决于其停止规则的随机化。这些属性使用硬币翻转的示例进行数值说明，即测试Bernoulli随机变量的成功概率。
A nonparametric variant of the Kiefer--Weiss problem is proposed and investigated. In analogy to the classical Kiefer--Weiss problem, the objective is to minimize the maximum expected sample size of a sequential test. However, instead of taking the maximum over a parametric family of distributions, it is taken over all distributions defined on the given sample space. Two optimality conditions are stated, one necessary and one sufficient. The latter is based on existing results on a more general minimax problem in sequential detection. These results are specialized and made explicit in this paper. It is shown that the nonparametric Kiefer--Weiss test is distinctly different from its parametric counterpart and admits non-standard, arguably counterintuitive properties. In particular, it can be nontruncated and critically depends on its stopping rules being randomized. These properties are illustrated numerically using the example of coin flipping, that is, testing the success probability of a Bernoulli random variable.
