Local shrinkage rules, Levy processes and regularized regression

• 成果类型: Article
• 署名作者: Polson, Nicholas G.; Scott, James G.
• 署名单位: University of Texas System; University of Texas Austin; University of Chicago
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2011.01015.x
• 发表日期: 2012
• 页码: 287-311
• 关键词: nonconcave penalized likelihood; variable-selection; posterior moments; distributions; mixtures; BAYES

摘要

. 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.