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Bayesian estimation of constrained mean-covariance of normal distributions

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  • Kundu, Anupam
  • Pourahmadi, Mohsen

Abstract

We study estimation of the mean-covariance under the joint constraint Σμ=μ for a multivariate normal. A reparametrized structured covariance is proposed through spectral decomposition of Σ involving μ, reducing the number of parameters. We approximate MLE by maximizing a lower bound of a profile likelihood and follow a similar strategy for Bayesian estimation. The MLE approximation performs the best.

Suggested Citation

  • Kundu, Anupam & Pourahmadi, Mohsen, 2023. "Bayesian estimation of constrained mean-covariance of normal distributions," Statistics & Probability Letters, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:stapro:v:194:y:2023:i:c:s0167715222002589
    DOI: 10.1016/j.spl.2022.109745
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    3. Peter D. Hoff, 2009. "A hierarchical eigenmodel for pooled covariance estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 971-992, November.
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