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Global-Local Shrinkage Priors for Asymptotic Point and Interval Estimation of Normal Means under Sparsity

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  • Zikun Qin

    (University of Florida)

  • Malay Ghosh

    (University of Florida)

Abstract

The paper addresses asymptotic estimation of normal means under sparsity. The primary focus is estimation of multivariate normal means where we obtain exact asymptotic minimax error under global-local shrinkage prior. This extends the corresponding univariate work of Ghosh and Chakrabarti (2017). In addition, we obtain similar results for the Dirichlet-Laplace prior as considered in Bhattacharya et al. (2015). Also, following van der Pas et al. (2017), we have been able to derive credible sets for multivariate normal means under global-local priors.

Suggested Citation

  • Zikun Qin & Malay Ghosh, 2024. "Global-Local Shrinkage Priors for Asymptotic Point and Interval Estimation of Normal Means under Sparsity," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 93-137, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00315-9
    DOI: 10.1007/s13171-023-00315-9
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    References listed on IDEAS

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    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    2. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
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