Polson, Nicholas G.; Scott, James G. Local shrinkage rules, Lévy processes and regularized regression. (English) Zbl 1411.62209 J. R. Stat. Soc., Ser. B, Stat. Methodol. 74, No. 2, 287-311 (2012). Summary: We use Lévy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter \(\beta=(\beta_1,\ldots,\beta_p)\) 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. Cited in 21 Documents MSC: 62J07 Ridge regression; shrinkage estimators (Lasso) 62H25 Factor analysis and principal components; correspondence analysis 62F12 Asymptotic properties of parametric estimators 60G51 Processes with independent increments; Lévy processes Keywords:Lévy processes; normal scale mixtures; partial least squares; principal components regression; shrinkage; sparsity PDFBibTeX XMLCite \textit{N. G. Polson} and \textit{J. G. Scott}, J. R. Stat. Soc., Ser. B, Stat. Methodol. 74, No. 2, 287--311 (2012; Zbl 1411.62209) Full Text: DOI arXiv