Authors:
Leonidas Sakalauskas
and
Ingrida Vaiciulyte
Affiliation:
Vilnius University, Lithuania
Keyword(s):
Monte – Carlo Markov chain, Skew t distribution, Maximum likelihood, Gaussian approximation, EM – algorithm, Testing hypothesis.
Related
Ontology
Subjects/Areas/Topics:
Agents
;
Artificial Intelligence
;
Bioinformatics
;
Biomedical Engineering
;
Enterprise Information Systems
;
Information Systems Analysis and Specification
;
Knowledge Discovery and Information Retrieval
;
Knowledge-Based Systems
;
Methodologies and Technologies
;
Operational Research
;
Optimization
;
Simulation
;
Stochastic Processes
;
Symbolic Systems
Abstract:
The present paper describes the Monte – Carlo Markov Chain (MCMC) method for estimation of skew t – distribution. The density of skew t – distribution is obtained through a multivariate integral, using representation of skew t – distribution by a mixture of multivariate skew – normal distribution with the covariance matrix, depending on the parameter, distributed according to the inverse – gamma distribution. Next, the MCMC procedure is constructed for recurrent estimation of skew t – distribution, following the maximum likelihood method, where the Monte – Carlo sample size is regulated to ensure the convergence and to decrease the total amount of Monte – Carlo trials, required for estimation. The confidence intervals of Monte – Carlo estimators are introduced because of their asymptotic normality. The termination rule is also implemented by testing statistical hypotheses on an insignificant change of estimates in two steps of the procedure.