Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 74, Issue -, Pages 287-311Publisher
WILEY
DOI: 10.1111/j.1467-9868.2011.01015.x
Keywords
Levy processes; Normal scale mixtures; Partial least squares; Principal components regression; Shrinkage; Sparsity
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. We use Levy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter as p grows large. This generalizes the class of localglobal 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.
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