Local shrinkage rules, Lévy processes and regularized regression

Abstract

We use Lévy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter as p grows large. This generalizes the class of local-global shrinkage rules based on scale mixtures of normals, illuminates new connections between disparate methods and leads to new results for computing posterior means and modes under a wide class of priors. We extend this framework to large-scale regularized regression problems where p>n, and we provide comparisons with other methodologies. © 2011 Royal Statistical Society.