文章基本信息

标题：Resampling Methods for the Nonparametric and Generalized Behrens-Fisher Problems
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作者：nsgar Steland RWTH Aachen University, Aachen ; Germany Appaswamy R. Padmanabhan Universit Sains Malaysia, Penang ; Malaysia Monash University, Clayton 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2011
卷号：73
期号：02
页码：267--302
出版社：Indian Statistical Institute
摘要：Dening a location parameter as a generalization of the median, a robust test is proposed for (a) the nonparametric Behrens-Fisher problem, where the underlying distributions may have di erent scales and could be skewed, and (b) the generalized Behrens-Fisher problem, where the distributions may even have di erent shapes. We propose to bootstrap a signed rank statistic based on di erences of sample values and derive rigorous bootstrap central limit theorems for its probabilistic justication, allowing for the so-called m-out-of-n bootstrap. The location parameter of interest is the pseudo-median of the distribution of the di erence between a control measure- ment and an observation from the treatment group. It reduces to (a) the shift in the two sample location model and (b) the di erence between the centers of symmetry in the nonparametric Behrens-Fisher model, under the additional assumption that the distributions are symmetric. Due to its importance for applications, we also extend our results to an ANOVA design where each treatment is compared with the control group. Finally, we compare our test with competitors on the basis of theory as well as simulation studies. It turns out that our approach yields a substantial improvement for distributions close to the generalized extreme value type, which makes it attrac- tive for applications in engineering as well as nance. Several heteroscedastic data sets from electrical engineering, astro physics, energy research, analytical chemistry and psychology are used to illustrate our solution.
关键词：Bootstrap, central limit theorem, generalized extreme value distribution, heteroscedasticity, signed-rank statistics, U-statistics.