Journal
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume 53, Issue 1, Pages 90-112Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2022.2076119
Keywords
Confidence bias; confidence error; confidence region; multiple regression; permutation inference
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The article introduces the application of permutation inference distribution in multiple regression, which can be used for hypothesis testing and confidence interval construction with relatively low computational burden. The results show that PID confidence regions are asymptotically ellipsoidal and exact.
The permutation inference distribution (PID) introduced in Wu and Vos (2019), The Journal of Nonparametric Statistics 31(3), 722-742) is extended to the joint PID for multiple regression. The joint PID is used for both hypothesis testing and the construction of confidence regions and its computational burden is similar to that of conducting a single hypothesis test. Asymptotic normality results show that PID confidence regions are asymptotically ellipsoidal and exact. In finite samples, the PID confidence regions can be used to check the fidelity of normal approximations. In some cases, normal theory-based confidence regions may be adjusted to approach nominal confidence errors. Simulation studies and real data applications are used to evaluate inferences obtained from the PID.
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