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Stat Sin. 2013 Jan 1;23(1):119-143.

GENERALIZED DOUBLE PARETO SHRINKAGE.

Author information

1
SAS Institute Inc., Durham, NC 27513, USA, artin.armagan@sas.com.
2
Department of Statistical Science, Duke University, Durham, NC 27708, USA, dunson@stat.duke.edu.
3
Department of Statistics, Seoul National University, Seoul, 151-747, Korea, leejyc@gmail.com.

Abstract

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors. While it has a spike at zero like the Laplace density, it also has a Student's t-like tail behavior. Bayesian computation is straightforward via a simple Gibbs sampling algorithm. We investigate the properties of the maximum a posteriori estimator, as sparse estimation plays an important role in many problems, reveal connections with some well-established regularization procedures, and show some asymptotic results. The performance of the prior is tested through simulations and an application.

KEYWORDS:

Heavy tails; LASSO; high-dimensional data; maximum a posteriori estimation; relevance vector machine; robust prior; shrinkage estimation

PMID:
24478567
PMCID:
PMC3903426

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