Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory solutions for estimation and testing problems. A general population Monte Carlo algorithm is proposed which: (1) exploits the latent structure stochastic representation of skew-normal random variables to provide a full Bayesian analysis of the model; and (2) accounts for the presence of constraints in the parameter space. The proposed approach can be defined as weakly informative, since the prior distribution approximates the actual reference prior for the shape parameter vector. Results are compared with the existing classical solutions and the practical implementation of the algorithm is illustrated via a simulation study and a real data example. A generalization to the matrix variate regression model with skew-normal error is also presented.

Liseo, B., Parisi, A. (2013). Bayesian inference for the multivariate skew-normal model: a population Monte Carlo approach. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 63, 125-138 [10.1016/j.csda.2013.02.007].

Bayesian inference for the multivariate skew-normal model: a population Monte Carlo approach

PARISI, ANTONIO
2013-01-01

Abstract

Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory solutions for estimation and testing problems. A general population Monte Carlo algorithm is proposed which: (1) exploits the latent structure stochastic representation of skew-normal random variables to provide a full Bayesian analysis of the model; and (2) accounts for the presence of constraints in the parameter space. The proposed approach can be defined as weakly informative, since the prior distribution approximates the actual reference prior for the shape parameter vector. Results are compared with the existing classical solutions and the practical implementation of the algorithm is illustrated via a simulation study and a real data example. A generalization to the matrix variate regression model with skew-normal error is also presented.
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore SECS-S/01 - STATISTICA
Settore SECS-S/03 - STATISTICA ECONOMICA
English
Con Impact Factor ISI
Bayes factor; matrix variate regression; objective Bayes inference; population Monte Carlo; reference prior; skewness
Liseo, B., Parisi, A. (2013). Bayesian inference for the multivariate skew-normal model: a population Monte Carlo approach. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 63, 125-138 [10.1016/j.csda.2013.02.007].
Liseo, B; Parisi, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/73927
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