Asymptotic theory of the adaptive Sparse Group Lasso

Benjamin Poignard ()
Additional contact information
Benjamin Poignard: Osaka University

Annals of the Institute of Statistical Mathematics, 2020, vol. 72, issue 1, No 14, 297-328

Abstract: Abstract We study the asymptotic properties of a new version of the Sparse Group Lasso estimator (SGL), called adaptive SGL. This new version includes two distinct regularization parameters, one for the Lasso penalty and one for the Group Lasso penalty, and we consider the adaptive version of this regularization, where both penalties are weighted by preliminary random coefficients. The asymptotic properties are established in a general framework, where the data are dependent and the loss function is convex. We prove that this estimator satisfies the oracle property: the sparsity-based estimator recovers the true underlying sparse model and is asymptotically normally distributed. We also study its asymptotic properties in a double-asymptotic framework, where the number of parameters diverges with the sample size. We show by simulations and on real data that the adaptive SGL outperforms other oracle-like methods in terms of estimation precision and variable selection.

Keywords: Asymptotic normality; Consistency; Oracle property (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10463-018-0692-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0692-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-018-0692-7

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().