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

We study full Bayesian procedures for high-dimensional linear regression. adopt data-dependent empirical priors introduced in Martin et al. (Bernoulli 23(3):1822–1847, 2017). In their paper, these have nice posterior contraction properties and are easy to compute. Our paper extend theoretical results the case of unknown error variance . Under proper sparsity assumption, we achieve model selection consistency, rates as well Bernstein von-Mises theorem by analyzing multivariate t-distribution.