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Local shrinkage rules, Lévy processes and regularized regression
Author(s) -
Polson Nicholas G.,
Scott James G.
Publication year - 2012
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2011.01015.x
Subject(s) - shrinkage , prior probability , regression , class (philosophy) , scale (ratio) , mathematics , computer science , mathematical optimization , artificial intelligence , statistics , bayesian probability , geography , cartography
Summary. 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.