Rank-based procedures in factorial designs: hypotheses about non-parametric treatment effects

• 成果类型: Article
• 署名作者: Brunner, Edgar; Konietschke, Frank; Pauly, Markus; Puri, Madan L.
• 署名单位: University of Gottingen; University of Texas System; University of Texas Dallas; Ulm University; Indiana University System; Indiana University Bloomington
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12229
• 发表日期: 2017
• 页码: 1463-1485
• 关键词: mann-whitney test; multiple comparison procedures; probabilistic index; permutation tests; statistics

摘要

Existing tests for factorial designs in the non-parametric case are based on hypotheses formulated in terms of distribution functions. Typical null hypotheses, however, are formulated in terms of some parameters or effect measures, particularly in heteroscedastic settings. Here this idea is extended to non-parametric models by introducing a novel non-parametric analysis-of-variance type of statistic based on ranks or pseudoranks which is suitable for testing hypotheses formulated in meaningful non-parametric treatment effects in general factorial designs. This is achieved by a careful detailed study of the common distribution of rank-based estimators for the treatment effects. Since the statistic is asymptotically not a pivotal quantity we propose three different approximation techniques, discuss their theoretic properties and compare them in extensive simulations together with two additional Wald-type tests. An extension of the presented idea to general repeated measures designs is briefly outlined. The rank- and pseudorank-based procedures proposed maintain the preassigned type I error rate quite accurately, also in unbalanced and heteroscedastic models.