Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions

Sheng Wang; Dale L Zimmerman; Patrick Breheny

doi:10.1016/j.jmva.2020.104639

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Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions

Journal article

Peer reviewed

Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions

Sheng Wang, Dale L Zimmerman and Patrick Breheny

Journal of multivariate analysis, Vol.179, p.104639

09/2020

DOI: 10.1016/j.jmva.2020.104639

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Abstract

The multivariate skew normal (MSN) and multivariate skew t (MST) distributions have received considerable attention in the past two decades because of their appealing mathematical properties and their usefulness for modeling skewed data. We develop sparse regularization methodology for estimating the skewness parameters of these two distributions. This methodology facilitates skewness selection, i.e., the identification of those marginal indices of skewness, if any, that are equal to zero. Obstacles that render skewness selection infeasible for existing parameterizations of the two distributions are described, and a new parameterization that permits the circumvention of those obstacles is introduced. A penalized likelihood method for sparsity-based regularized skewness estimation using the new parameterization is proposed. Model selection consistency and the oracle property of the method are established. A simulation study demonstrates that the method is reasonably effective for skewness selection and, because of inclusion of a ridge penalty, is more effective at preventing the divergence of the shape parameter in small samples than the Q-penalty approach of Azzalini and Arellano-Valle (2013). The simulation study demonstrates further that our method may improve the estimation of all parameters of the MSN and MST distributions, not merely the skewnesses, when some of the skewnesses are zero.

Multivariate skew [formula omitted] distribution

Multivariate skew normal distribution

Penalized likelihood

Regularization

Skewness

Sparsity

Details

Title: Subtitle: Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions
Creators: Sheng Wang - Blue Yonder, Inc., Coppell, TX, USA
Dale L Zimmerman - University of Iowa
Patrick Breheny - University of Iowa
Resource Type: Journal article
Publication Details: Journal of multivariate analysis, Vol.179, p.104639
DOI: 10.1016/j.jmva.2020.104639
ISSN: 0047-259X
eISSN: 1095-7243
Publisher: Elsevier Inc
Language: English
Date published: 09/2020
Academic Unit: Statistics and Actuarial Science; Biostatistics; Internal Medicine
Record Identifier: 9984257612702771

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