A unified class of penalties with the capability of producing a differentiable alternative to l1 norm penalty. Issue 22 (17th November 2019)

• Record Type: Journal Article
• Authors: Haselimashhadi, Hamed
• Is Part Of: Communications in statistics. Volume 48:Issue 22(2019)
• Page Start: 5530
• Page End: 5545
• Publication Date: 2019-11-17
• Subjects: Likelihood regularization -- generalised information criterion -- lasso -- SCAD -- differentiable penalty; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1515362
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: This article presents a class of novel penalties that are defined under a unified framework, which includes lasso, SCAD and ridge as special cases, and novel functions, such as the asymmetric quantile check function. The proposed class of penalties is capable of producing alternative differentiable penalties to lasso. We mainly focus on this case and show its desirable properties, propose an efficient algorithm for the parameter estimation and prove the theoretical properties of the resulting estimators. Moreover, we exploit the differentiability of the penalty function by deriving a novel Generalized Information Criterion (GIC) for model selection. The method is implemented in the R package DLASSO freely available from CRAN, http://CRAN.R-project.org/package=DLASSO .