An objective non-local prior for skew-symmetric models

TL;DR

This paper introduces an objective non-local prior for testing symmetry versus skew-symmetric models, providing a hyperparameter-free, informative approach suitable for normality testing with simulations and real data.

Contribution

It develops a new non-local prior for skew-symmetric models that is automatically constructed without user hyperparameters, enhancing symmetry testing methods.

Findings

The prior performs well in simulation studies.

It effectively distinguishes symmetric from skew-symmetric distributions.

Application to real data demonstrates practical utility.

Abstract

We propose an objective non-local prior for testing symmetry against skew-symmetric alternatives. The prior is derived through a formal construction rule by assigning a uniform distribution to a discrepancy-based measure of the shape parameter's effect. This approach avoids the need for user-specified hyperparameters and produces a weakly informative prior tailored to the skew-symmetric family. We illustrate the use of the proposed prior in the context of testing normality against skew-normal alternatives through both a simulation study and a real-data application.