Regularized multivariate regression models with skew-t error distributions

Lianfu Chen, Mohsen Pourahmadi, Mehdi Maadooliat

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We consider regularization of the parameters in multivariate linear regression models with the errors having a multivariate skew-t distribution. An iterative penalized likelihood procedure is proposed for constructing sparse estimators of both the regression coefficient and inverse scale matrices simultaneously. The sparsity is introduced through penalizing the negative log-likelihood by adding L1-penalties on the entries of the two matrices. Taking advantage of the hierarchical representation of skew-t distributions, and using the expectation conditional maximization (ECM) algorithm, we reduce the problem to penalized normal likelihood and develop a procedure to minimize the ensuing objective function. Using a simulation study the performance of the method is assessed, and the methodology is illustrated using a real data set with a 24-dimensional response vector. © 2014 Elsevier B.V.
Original languageEnglish (US)
Pages (from-to)125-139
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume149
DOIs
StatePublished - Jun 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: We would like to thank two referees for their constructive comments and suggestions. The second author was supported by the National Science Foundation (Grants DMS-0906252 and DMS-1309586), and the third author was partially supported by King Abdullah University of Science and Technology (Grant KUS-CI-016-04).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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