On the Independence Jeffreys prior for skew--symmetric models with applications

TL;DR

This paper analyzes the Jeffreys prior for the skewness parameter in skew-symmetric models, establishing its properties, calculating the independence Jeffreys prior for certain cases, and demonstrating its application with real data.

Contribution

It provides a detailed study of the Jeffreys prior for skewness, including its properties, the independence Jeffreys prior for models with unknown location and scale, and conditions for posterior existence.

Findings

The Jeffreys prior is symmetric, proper, with tails decaying as O(λ^{-3/2})

Conditions for posterior existence are established for skew-symmetric scale mixtures of normals

Applications demonstrate the practical usefulness of the theoretical results

Abstract

We study the Jeffreys prior of the skewness parameter of a general class of scalar skew--symmetric models. It is shown that this prior is symmetric about 0, proper, and with tails $O(\lambda^{-3/2})$ under mild regularity conditions. We also calculate the independence Jeffreys prior for the case with unknown location and scale parameters. Sufficient conditions for the existence of the corresponding posterior distribution are investigated for the case when the sampling model belongs to the family of skew--symmetric scale mixtures of normal distributions. The usefulness of these results is illustrated using the skew--logistic model and two applications with real data.