High-dimensional properties for empirical priors in linear regression with unknown error variance

2022/02/11 by Fang, Xiao, Ghosh, Malay
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2202.05419

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.

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