Permutation inference distribution for linear regression and related models. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Wu, Qiang; Vos, Paul
• Is Part Of: Journal of nonparametric statistics. Volume 31:Issue 3(2019)
• Page Start: 722
• Page End: 742
• Publication Date: 2019-07-03
• Subjects: Confidence bias -- confidence error -- confidence interval -- linear regression -- permutation inference; 62G08 -- 62G09 -- 62G20; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2019.1632306
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: For linear regression and related models, a permutation inference distribution (PID) is introduced. Like the confidence distribution in the Bayesian/Fiducial/Frequentist inference framework, the PID allows the construction of both confidence intervals and p -values. For two-sample problems and pairwise comparisons in ANOVA models, a fast Fourier transformation method can be used to find the exact PID. In general, however, random permutations are required except for small samples where all n ! permutations can be generated. Simulation studies and real data applications are used to evaluate inferences obtained from the PID. PID methods are close to standard parametric methods when the errors are iid and normal. For skewed and heavy tailed errors, PID methods are superior to bootstrap and standard parametric methods.