On the independence Jeffreys prior for skew-symmetric models

We study the Jeffreys prior of the skewness parameter of a general class of scalar skew-symmetric models. We show that this prior is symmetric, proper, and with tails O(|λ|−3/2) under mild regularity conditions. We also calculate the independence Jeffreys prior for the case with unknown location and scale parameters, and investigate conditions for the propriety of the corresponding posterior distribution.