Sparsely restricted penalized estimators

Hüseyin Güler and Ebru Ozgur Guler

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 7, 1656-1670

Abstract: Parameters of a linear regression model might be estimated with Ordinary Least Squares (OLS). If there are linear restrictions on model parameters, it is possible to use Restricted Least Squares (RLS). Both OLS and RLS fail when the number of predictors is large and not suitable for model selection in a sparse model. In contrast to OLS and RLS, Least Absolute Shrinkage and Selection Operator (LASSO) and Bridge estimators perform well in sparse models and can be used for model selection and estimation, simultaneously. A Restricted LASSO (RLASSO) estimator is proposed in the literature recently but it doesn’t provide sparse solutions. In this paper, we propose new sparsely restricted penalized estimators called Sparsely Restricted LASSO (SRL) and Sparsely Restricted Bridge (SRB) based on RLASSO and Restricted Bridge (RBridge). We show that SRL and SRB produces sparse solutions while satisfying restrictions of model parameters. We compare aforementioned estimators with Monte Carlo simulations. We also use prostate cancer dataset that is widely used in the literature for a numerical application. Our comparisons show that SRL and SRB outperform the remaining estimators in terms of model selection performance and mean squared error.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2019.1682164 (text/html)
Access to full text is restricted to subscribers.

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:taf:lstaxx:v:50:y:2021:i:7:p:1656-1670

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2019.1682164

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().