High-dimensional properties for empirical priors in linear regression with unknown error variance
Statistics Theory
2022-02-14 v1 Statistics Theory
Abstract
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper extend their theoretical results to the case of unknown error variance . Under proper sparsity assumption, we achieve model selection consistency, posterior contraction rates as well as Bernstein von-Mises theorem by analyzing multivariate t-distribution.
Cite
@article{arxiv.2202.05419,
title = {High-dimensional properties for empirical priors in linear regression with unknown error variance},
author = {Xiao Fang and Malay Ghosh},
journal= {arXiv preprint arXiv:2202.05419},
year = {2022}
}