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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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    References listed on IDEAS

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    1. Howard D. Bondell & Brian J. Reich, 2012. "Consistent High-Dimensional Bayesian Variable Selection via Penalized Credible Regions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1610-1624, December.
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    3. Valen E. Johnson & David Rossell, 2012. "Bayesian Model Selection in High-Dimensional Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 649-660, June.
    4. L Hong & T A Kuffner & R Martin, 2018. "On overfitting and post-selection uncertainty assessments," Biometrika, Biometrika Trust, vol. 105(1), pages 221-224.
    5. Ryan Martin & Bo Ning, 2020. "Empirical Priors and Coverage of Posterior Credible Sets in a Sparse Normal Mean Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 477-498, August.
    6. Nicholas Syring & Ryan Martin, 2019. "Calibrating general posterior credible regions," Biometrika, Biometrika Trust, vol. 106(2), pages 479-486.
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