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

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, Pati, Pillai, and Dunson (2015). Also, following van der Pas, Szabo, and van der Vaart (2017), we have been able to derive credible sets for multivariate normal means under global-local priors.

This is an updated version of the published paper. Sankhya A (2023)

References in corpus (3)

• Needles and Straw in a Haystack: Posterior concentration for possibly sparse sequences
• The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors
• Contributed Discussion to Uncertainty Quantification for the Horseshoe by Stéphanie van der Pas, Botond Szabó and Aad van der Vaart