Regularized multivariate regression models with skew-t error distributions
KAUST Grant NumberKUS-CI-016-04
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AbstractWe 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.
CitationChen L, Pourahmadi M, Maadooliat M (2014) Regularized multivariate regression models with skew-t error distributions. Journal of Statistical Planning and Inference 149: 125–139. Available: http://dx.doi.org/10.1016/j.jspi.2014.02.001.
SponsorsWe 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).