Format of Original
Journal of Statistical Planning and Inference
Original Item ID
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.
Chen, Lianfu; Pourahmadi, Mohsen; and Maadooliat, Mehdi, "Regularized Multivariate Regression Models with Skew-t Error Distributions" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 225.
Accepted version. Journal of Statistical Planning and Inference, Vol. 149 (June 2014): 125-129. DOI. © 2014 Elsevier. Used with permission.