论文标题
一种用于精确多项式测试的简单算法
A Simple Algorithm for Exact Multinomial Tests
论文作者
论文摘要
这项工作提出了一种计算精确多项式测试接受区域的新方法。从此得出了一种算法，该算法找到了简单多项性假设测试的精确p值。使用离散凸分析中的概念，该方法被证明是针对各种流行的测试统计数据（包括皮尔逊的卡方和对数类样比率）准确的。通过完全列举样品空间，提出的算法在天真的方法上大大改善。但是，随着运行时在可能的结果数量中呈指数增长，它的使用仅限于具有少数类别的多项式分布。 该方法应用于模拟研究，并概述了多项式测试在预测评估中的使用。此外，研究并讨论了使用概率排序的测试统计量的属性，该属性被研究和讨论了一些作者称为“确切的多项式测试”。该算法是在随附的R软件包精确度词中实现的。
This work proposes a new method for computing acceptance regions of exact multinomial tests. From this an algorithm is derived, which finds exact p-values for tests of simple multinomial hypotheses. Using concepts from discrete convex analysis, the method is proven to be exact for various popular test statistics, including Pearson's chi-square and the log-likelihood ratio. The proposed algorithm improves greatly on the naive approach using full enumeration of the sample space. However, its use is limited to multinomial distributions with a small number of categories, as the runtime grows exponentially in the number of possible outcomes. The method is applied in a simulation study and uses of multinomial tests in forecast evaluation are outlined. Additionally, properties of a test statistic using probability ordering, referred to as the "exact multinomial test" by some authors, are investigated and discussed. The algorithm is implemented in the accompanying R package ExactMultinom.
