The EAS approach to variable selection for multivariate response data in high-dimensional settings

Abstract

In this paper, we extend the epsilon admissible subsets (EAS) model selection approach, from its original construction in the high-dimensional linear regression setting, to an EAS framework for performing group variable selection in the high-dimensional multivariate regression setting. Assuming a matrix-Normal linear model we show that the EAS strategy is asymptotically consistent if there exists a sparse, true data generating set of predictors. Nonetheless, our EAS strategy is designed to estimate a posterior-like, generalized fiducial distribution over a parsimonious class of models in the setting of correlated predictors and/or in the absence of a sparsity assumption. The effectiveness of our approach, to this end, is demonstrated empirically in simulation studies, and is compared to other state-of-the-art model/variable selection procedures.

On the proof of posterior contraction for sparse generalized linear models with multivariate responses

“…We note that since the publication of Bai and Ghosh [5], further progress has been made on the theoretical study of Gaussian multivariate linear regression. For example, Ning et al [25] and Zhang and Ghosh [28] proved posterior contraction rates for the regression coefficients matrix B n when p n, while Koner and Williams [23] proved model selection consistency for multivariate linear regression when p n. These other works only deal with responses that are Gaussian, and their results cannot be applied to non-Gaussian responses such as binary or count data.…”