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

Zikun Qin () and Malay Ghosh ()
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Zikun Qin: University of Florida
Malay Ghosh: University of Florida

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 4, 93-137

Abstract: 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.

Keywords: Exponential-inverse-gamma; Beta prime priors; Concentration inequalities; Exact rate; Minimax (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-023-00315-9

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