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Post-processed posteriors for sparse covariances

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  • Lee, Kwangmin
  • Lee, Jaeyong

Abstract

We consider Bayesian inference of sparse covariance matrices and propose a post-processed posterior. This method consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior without considering the sparse structural assumption. The posterior samples are transformed in the second step to satisfy the sparse structural assumption through a generalized thresholding function. This non-traditional Bayesian procedure is justified by showing that the post-processed posterior attains the optimal minimax rates under the spectral norm loss in high-dimensional settings. We also propose the post-processed posterior for contaminated data and apply it to the estimation of the sparse idiosyncratic covariance of the approximate factor model. The advantages of our method are demonstrated via a simulation study and a real data analysis with S&P 500 data.

Suggested Citation

  • Lee, Kwangmin & Lee, Jaeyong, 2023. "Post-processed posteriors for sparse covariances," Journal of Econometrics, Elsevier, vol. 236(1).
    • Handle: RePEc:eee:econom:v:236:y:2023:i:1:s0304407623001914
    DOI: 10.1016/j.jeconom.2023.105475
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    References listed on IDEAS

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