Estimation of skew t-distribution by Monte-Carlo Markov chain approach

Abstract

The Monte-Carlo Markov Chain (MCMC) method for estimation of skew t-distribution is developed in the paper. Using the representation of the skew t- distribution is represented by multivariate skew { normal distribution with covari- ance matrix depending on parameter distributed according to inverse { gamma distribution (Azzalini and Genton, 2008), the density of skew t-distribution is expressed through multivariate integral. Next, the MCMC procedure is con- structed for recurrent estimation of skew t-distribution by maximum likelihood, where the Monte-Carlo sample size is regulated so that to ensure the convergence and to decrease the total amount of Monte-Carlo trials. The conЇdence intervals of Monte-Carlo estimators are introduced because the asymptotic distribution of Monte-Carlo estimators is Gaussian according to the CLT and the termination rule is implemented testing statistical hypotheses about insigniЇcant change of estimates in two steps of the procedure (Sakalauskas, 2000).