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

Author

Listed:
  • Xiao Fang

    (University of Florida)

  • Malay Ghosh

    (University of Florida)

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.

Suggested Citation

  • Xiao Fang & Malay Ghosh, 2024. "High-dimensional properties for empirical priors in linear regression with unknown error variance," Statistical Papers, Springer, vol. 65(1), pages 237-262, February.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:1:d:10.1007_s00362-022-01390-0
    DOI: 10.1007/s00362-022-01390-0
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