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

Xiao Fang () and Malay Ghosh ()
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Xiao Fang: University of Florida
Malay Ghosh: University of Florida

Statistical Papers, 2024, vol. 65, issue 1, No 10, 237-262

Abstract: Abstract We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in Martin et al. (Bernoulli 23(3):1822–1847, 2017). 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.

Keywords: Bernstein von-Mises theorem; Model selection consistency; Multivariate t-distribution; Posterior contraction rate (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-022-01390-0

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