Plausibility regions on the skewness parameter of skew normal distributions based on inferential models

Abstract

Inferential models (IMs) are new methods of statistical inference. They have several advantages: (1) They are free of prior distributions; (2) They rely on data. In this paper, 100(1 − α)% plausibility regions of the skewness parameter of skew-normal distributions are constructed by using IMs, which are the counterparts of classical confidence intervals in IMs.