Generalized double Pareto shrinkage

Details Generalized double Pareto shrinkage Generalized double Pareto shrinkage

2011-04-05

arxiv.org/abs/1104.0861v3

Statistics

Methodology

Scientific paper

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 application to real data.

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