The nonparametric Behrens-Fisher problem: Asymptotic theory and a small-sample approximation
The nonparametric Behrens-Fisher problem: Asymptotic theory and a small-sample approximation
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DOI：
10.1002/(sici)1521-4036(200001)42:1
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发表时间：
2000-01-01
影响因子：
1.7
通讯作者：
Munzel, U
中科院分区：
文献类型：
--
作者：
Brunner, E;Munzel, U
在一个非参数模型中研究了两个样本下的广义Beynolds-Fisher问题。它不假设基础分布函数是连续的，以便可以处理具有任意关系的数据。考虑秩余，其中通过使用所有观测值的秩以及每个样本内的秩来一致地估计渐近方差。估计量的一致性在附录中得到。对于小样本（n（1），n（2）大于或等于10），一个简单的近似中心t-分布的建议，其中的自由度取自Satterthwaite-Smith-Welch近似的参数Beethers-Fisher问题。通过模拟研究表明，Wilcoxon-Mann-Whitney检验可以是保守的，也可以是自由的，这取决于样本容量的比例和潜在分布函数的方差。然而，对于建议的近似值，事实证明，名义水平保持得相当准确。建议的非参数程序应用于临床试验的数据集。此外，给出了非参数治疗效应的置信区间。
A generalization of the Behrens-Fisher problem for two samples is examined in a nonparametric model. It is not assumed that the underlying distribution functions are continuous so that data with arbitrary ties can be handled. A rank rest is considered where the asymptotic variance is estimated consistently by using the ranks over all observations as well as the ranks within each sample. The consistency of the estimator is derived in the appendix. For small samples (n(1), n(2) greater than or equal to 10), a simple approximation by a central t-distribution is suggested where the degrees of freedom are taken from the Satterthwaite-Smith-Welch approximation in the parametric Behrens-Fisher problem. It is demonstrated by means of a simulation study that the Wilcoxon-Mann-Whitney-test may be conservative or liberal depending on the ratio of the sample sizes and the variances of the underlying distribution functions. For the suggested approximation, however, it turns out that the nominal level is maintained rather accurately. The suggested nonparametric procedure is applied to a data set from a clinical trial. Moreover, a confidence interval for the nonparametric treatment effect is given.