论文标题
小样本中的非参数behrens-fisher问题
The nonparametric Behrens-Fisher problem in small samples
论文作者
论文摘要
尽管有关与Wilcoxon-Mann-Whitney测试相关的估算和估计量定义的文献似乎达成了一般共识，但对于如何最好地估计差异，似乎还不清楚。除了Wilcoxon-Mann-Whitney测试外，我们还审查了零假设和替代方案在一致的方差估计器方面的不同建议。此外，在样本量较小的情况下，已经提出了基于t分布的测试统计量分布的近似，已经提出了logit变换和置换方法。在T及t-approximation方面，我们对自由度的不同估计量进行了重点，我们对一系列场景进行了模拟，结果表明，不同方差估计器在控制I型错误率方面的性能很大程度上取决于异质分配模式和样本大小分配比例，而不是使用特定的分布型。总体而言，特定的T型抗性以及验证剂和Manevski的方差估计器最能保持名义意义水平
While there appears to be a general consensus in the literature on the definition of the estimand and estimator associated with the Wilcoxon-Mann-Whitney test, it seems somewhat less clear as to how best to estimate the variance. In addition to the Wilcoxon-Mann-Whitney test, we review different proposals of variance estimators consistent under both the null hypothesis and the alternative. Moreover, in case of small sample sizes, an approximation of the distribution of the test statistic based on the t-distribution, a logit transformation and a permutation approach have been proposed. Focussing as well on different estimators of the degrees of freedom as regards the t-approximation, we carried out simulations for a range of scenarios, with results indicating that the performance of different variance estimators in terms of controlling the type I error rate largely depends on the heteroskedasticity pattern and the sample size allocation ratio, not on the specific type of distributions employed. By and large, a particular t-approximation together with Perme and Manevski's variance estimator best maintains the nominal significance level
