Permutation Confidence Region for Regression Slopes and a Diagnostic Tool for the Central Limit Theorem

• Activity Number: 297 - Advances in Nonparametric Testing
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Qiang Wu* and Paul Vos
• Companies: East Carolina University and East Carolina University
• Keywords: confidence bias ; confidence error ; confidence interval ; linear regression ; permutation inference

Abstract

For linear regressions, a joint permutation inference distribution (PID) is introduced when the errors are assumed exchangeable. Like the confidence distribution in the Bayesian/Fiducial/Frequentist inference framework, the PID allows constructing confidence regions/intervals and p-values. In addition, a diagnostic tool based on the PID is proposed to assess the degree to which the Central Limit Theorem (CLT) applies. To construct the PID, random permutations are usually required except for small samples where all n! permutations can be generated. The permutation confidence regions/intervals and p-values obtained from the PID can be reported alternatively to the normal based procedures when there are evidence that the CLT may not apply. Simulation studies and real data applications are used to evaluate inferences obtained from the PID.