论文标题
从离散指数家庭取样时，Kiefer-Weiss问题的设计和绩效评估
Design and performance evaluation in Kiefer-Weiss problems when sampling from discrete exponential families
论文作者
论文摘要
在本文中，我们处理在顺序统计分析框架中测试假设的问题。主要问题是对Kiefer-Weiss问题中抽样计划的最佳设计和性能评估。 对于遵循离散指数家族的观察结果，我们为修改后的Kiefer-Weiss问题提供了最佳设计算法，并获得用于评估其性能，计算操作特征功能，平均样本数和某些相关特征的公式。这些公式覆盖了某种情况下，顺序概率比测试（SPRT）及其截短版本以及最佳的有限摩尼子顺序测试。 根据开发的算法，我们提出了一种最佳测试的构建方法及其对原始Kiefer-Weiss问题的绩效评估。 所有算法均以R编程语言的功能实现，并且可以从{\ tt https://github.com/tosinabase/kiefer-weiss}下载，其中二项式，POISSON和负二项式分布的功能易于获得。 最后，我们将Kiefer-Weiss解决方案与SPRT进行数值比较，并且具有相同级别的误差概率的固定样本大小测试。
In this paper, we deal with problems of testing hypotheses in the framework of sequential statistical analysis. The main concern is the optimal design and performance evaluation of sampling plans in the Kiefer-Weiss problems. For the observations which follow a discrete exponential family, we provide algorithms for optimal design in the modified Kiefer-Weiss problem, and obtain formulas for evaluating their performance, calculating operating characteristic function, average sample number, and some related characteristics. These formulas cover, as a particular case, the sequential probability ratio tests (SPRT) and their truncated versions, as well as optimal finite-horizon sequential tests. On the basis of the developed algorithms we propose a method of construction of optimal tests and their performance evaluation for the original Kiefer-Weiss problem. All the algorithms are implemented as functions in the R programming language and can be downloaded from {\tt https://github.com/tosinabase/Kiefer-Weiss}, where the functions for the binomial, Poisson, and negative binomial distributions are readily available. Finally, we make numerical comparisons of the Kiefer-Weiss solution with the SPRT and the fixed-sample-size test having the same levels of the error probabilities.
