Rank-based multiple test procedures and simultaneous confidence intervals
Rank-based multiple test procedures and simultaneous confidence intervals
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DOI：
10.1214/12-ejs691
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发表时间：
2012-01-01
影响因子：
1.1
通讯作者：
Hothorn, Ludwig A.
中科院分区：
文献类型：
--
作者：
Konietschke, Frank;Hothorn, Ludwig A.
我们研究了具有独立观测值的非平衡设计的同时秩方法。这些假设是根据纯粹的非参数治疗效应制定的。在这种情况下，我们推导出基于秩的多重对比检验程序和同时置信区间，其中考虑了检验统计量之间的相关性。因此，个体检验决策和同时置信区间是相容的。这意味着，每当单个假设被多重对比检验拒绝时，相应的同时置信区间不包括空值，即无治疗效应的假设值。该程序允许测试任意的纯非参数多重线性假设（例如，多对一，所有对，变点，甚至平均比较）。我们不假设数据的齐次方差;特别是，即使在零假设下，分布也可以具有不同的形状。因此，在这个统一的框架中，多个非参数的Beynolds-Fisher问题的解决方案。
We study simultaneous rank procedures for unbalanced designs with independent observations. The hypotheses are formulated in terms of purely nonparametric treatment effects. In this context, we derive rank-based multiple contrast test procedures and simultaneous confidence intervals which take the correlation between the test statistics into account. Hereby, the individual test decisions and the simultaneous confidence intervals are compatible. This means, whenever an individual hypothesis has been rejected by the multiple contrast test, the corresponding simultaneous confidence interval does not include the null, i.e. the hypothetical value of no treatment effect. The procedures allow for testing arbitrary purely nonparametric multiple linear hypotheses(e.g. many-to-one, all-pairs, changepoint, or even average comparisons). We do not assume homogeneous variances of the data; in particular, the distributions can have different shapes even under the null hypothesis. Thus, a solution to the multiple nonparametric Behrens-Fisher problem is presented in this unified framework.