MAXIMUM LIKELIHOOD ESTIMATION OF MULTIVARIATE SKEW T-DISTRIBUTION

Leonidas Sakalauskas, Ingrida Vaiciulyte

2012

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.

References

  1. Azzalini, A. and Capitanio, A. (2003). Distributions Generated by Perturbation of Symmetry with Emphasis on a Multivariate Skew t Distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65, 367 - 389.
  2. Azzalini, A. and Genton, M. G. (2008). Robust Likelihood Methods Based on the Skew - t and Related Distributions. International Statistical Review, 76 (1), 106 - 129.
  3. Cabral, C. R. B., Bolfarine, H. and Pereira, J. R. G. (2008). Bayesian Density Estimation using Skew Student-t-normal Mixtures. Computational Statistics and Data Analysis, 52 (12), 5075-5090.
  4. Kim, H. M. and Mallick B. K. (2003). Moments of Random Vectors with Skew t Distribution and their Quadratic Forms. Statistics & Probability Letters, 63, 417-423.
  5. Panagiotelis, A. and Smith, M. (2008). Bayesian Density Forecasting of Intraday Electricity Prices using Multivariate Skew t Distributions. International Journal of Forecasting, 24, 710-727.
  6. Rubinstein, R. Y. and Kroese, D. P. (2007). Simulation and the Monte Carlo Method (2nd ed.). New York: Wiley.
  7. Sakalauskas, L. (2000). Nonlinear Stochastic Optimization by Monte-Carlo Estimators. Informatica, 11 (4), 455- 468.
  8. Spall, J. C. (2003). Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control. New York: Wiley.
Download


Paper Citation


in Harvard Style

Sakalauskas L. and Vaiciulyte I. (2012). MAXIMUM LIKELIHOOD ESTIMATION OF MULTIVARIATE SKEW T-DISTRIBUTION . In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-8425-97-3, pages 200-203. DOI: 10.5220/0003727002000203


in Bibtex Style

@conference{icores12,
author={Leonidas Sakalauskas and Ingrida Vaiciulyte},
title={MAXIMUM LIKELIHOOD ESTIMATION OF MULTIVARIATE SKEW T-DISTRIBUTION},
booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2012},
pages={200-203},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003727002000203},
isbn={978-989-8425-97-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - MAXIMUM LIKELIHOOD ESTIMATION OF MULTIVARIATE SKEW T-DISTRIBUTION
SN - 978-989-8425-97-3
AU - Sakalauskas L.
AU - Vaiciulyte I.
PY - 2012
SP - 200
EP - 203
DO - 10.5220/0003727002000203