Box-type approximations in nonparametric factorial designs

• 成果类型: Article
• 署名作者: Brunner, E; Dette, H; Munk, A
• 署名单位: University of Gottingen; Ruhr University Bochum
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2965420
• 发表日期: 1997
• 页码: 1494-1502
• 关键词: Rank; MULTIVARIATE; statistics; tests

摘要

Linear rank statistics in nonparametric factorial designs are asymptotically normal and, in general, heteroscedastic. In a comprehensive simulation study, the asymptotic chi-squared law of the corresponding quadratic forms is shown to be a rather poor approximation of the finite-sample distribution. Motivated by this problem, we propose simple finite-sample size approximations for the distribution of quadratic forms in factorial designs under a normal heteroscedastic error structure. These approximations are based on an F distribution with estimated degrees of freedom that generalizes ideas of Patnaik and Box. Simulation studies show that the nominal level is maintained with high accuracy and in most cases the power is comparable to the asymptotic maximin Wald test. Data-driven guidelines are given to select the most appropriate test procedure. These ideas are finally transferred to nonparametric factorial designs where the same quadratic forms as in the parametric case are applied to the vector of averaged ranks. A simulation study shows that the corresponding nonparametric F-test keeps its level with high accuracy and has power comparable to that of the rank version of the likelihood statistic.