Inferential aspects of the skew-t distribution

This paper concerns likelihood inference for the skew $t$-distribution, which includes both the skew normal and the normal distributions as important special cases that occur when the degrees of freedom is infinite. Inference based on the skew $t$-model becomes problematic in these special cases for two reasons: the expected information matrix is singular; and the parameter corresponding to the degrees of freedom takes a value occurring at the boundary of its parameter space. For each of the special cases, a reparameterization is introduced that copes with these difficulties, thereby producing consistent estimators with known asymptotic properties. Inference for multiple linear regression models based on the skew $t$-distribution is also considered.