Asymptotic Permutation Tests in General Factorial Designs

• Activity Number: 497
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Frank Konietschke*
• Companies: The University of Texas at Dallas
• Keywords: Permutation Tests ; Linear Models ; Heteroscedasticity ; Studentized Statistics

Abstract

In general factorial designs where no homoscedasticity or a particular error distribution is assumed, the well known Wald-type statistic (WTS) is a simple asymptotically valid procedure. However, it is well known that it suffers from a poor finite sample approximation since the convergence to its ?2-limit distribution is quite slow. This gets even worse with an increasing number of factor levels. In this talk, we discuss a general permutation approach to improve the small sample behavior of the WTS maintaining its applicability to general settings as crossed or hierarchically nested designs. In particular, it is shown that this approach approximates the null distribution of the WTS not only under the null hypothesis but also under the alternative yielding an asymptotically valid permutation test which is even finitely exact under exchangeability. Finally, its small sample behavior is compared with competing procedures in an extensive simulation study. A real data example illustrates the application of the proposed methods.

References:

Pauly, M., Brunner, E., Konietschke, F. (2014). Journal of the Royal Statistical Society - Series B. DOI: 10.1111/rssb.12073