Online Program Home
My Program

Abstract Details

Activity Number: 62
Type: Topic Contributed
Date/Time: Sunday, July 31, 2016 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #320884
Title: Bayesian High-Dimensional Sparse Models with Unknown Symmetric Errors
Author(s): Lizhen Lin* and Minwoo Chae and David Dunson
Companies: The University of Texas and The University of Texas at Austin and Duke University
Keywords: Bayesian high-dimensional models ; Unknown symmetric error ; Sparse models ; Semiparametric BVM

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. Unknown error distribution is endowed with a symmetrized Dirichlet process mixture of normal prior. For the prior of regression coefficients, a mixture of point masses at zero and Laplace distributions is used. When the number of non-zero coefficients is of order $o(n^{-1/3})$ and the prior mass on it decreases exponentially, the marginal posterior distribution of regression coefficients is shown to contract at the optimal rate under compatibility conditions on the design matrix. The semiparametric Bernstein-von Mises theorem will be derived under stronger conditions.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2016 program

Copyright © American Statistical Association