Title: Bayesian sparse linear regression with unknown symmetric error
Authors: Minwoo Chae - Pohang University of Science and Technology (Korea, South) [presenting]
Lizhen Lin - The University of Notre Dame (United States)
David Dunson - Duke University (United States)
Abstract: Bayesian procedures for sparse linear regression are considered when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the prior on regression coefficients, a mixture of point masses at zero and continuous distributions is considered. Asymptotic behavior of the posterior is studied with diverging number of predictors. The compatibility and restricted eigenvalue conditions yield the optimal convergence rate of the regression coefficients in l1 and l2 norms, respectively. The convergence rate is adaptive to both the unknown sparsity level and the unknown symmetric error density. In addition, strong model selection consistency and a semi-parametric Bernstein-von Mises theorem are considered under slightly stronger conditions.