Regularized multivariate regression models with skew-t error distributions

Lianfu Chen; Mohsen Pourahmadi; Mehdi Maadooliat

doi:10.1016/j.jspi.2014.02.001

Regularized multivariate regression models with skew-t error distributions

Lianfu Chen, Mohsen Pourahmadi, Mehdi Maadooliat

Research output: Contribution to journal › Article › peer-review

16 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 language	English (US)
Pages (from-to)	125-139
Number of pages	15
Journal	Journal of Statistical Planning and Inference
Volume	149
DOIs	https://doi.org/10.1016/j.jspi.2014.02.001
State	Published - Jun 2014
Externally published	Yes

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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10.1016/j.jspi.2014.02.001

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title = "Regularized multivariate regression models with skew-t error distributions",

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. {\textcopyright} 2014 Elsevier B.V.",

author = "Lianfu Chen and Mohsen Pourahmadi and Mehdi Maadooliat",

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.",

year = "2014",

month = jun,

doi = "10.1016/j.jspi.2014.02.001",

language = "English (US)",

volume = "149",

pages = "125--139",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

publisher = "Elsevier B.V.",

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AU - Chen, Lianfu

AU - Pourahmadi, Mohsen

AU - Maadooliat, Mehdi

N1 - 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.

PY - 2014/6

Y1 - 2014/6

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/599488

UR - https://linkinghub.elsevier.com/retrieve/pii/S0378375814000081

UR - http://www.scopus.com/inward/record.url?scp=84899980350&partnerID=8YFLogxK

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DO - 10.1016/j.jspi.2014.02.001

M3 - Article

SN - 0378-3758

VL - 149

SP - 125

EP - 139

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

ER -

Regularized multivariate regression models with skew-t error distributions

Abstract

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