Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Unified LASSO Estimation by Least Squares Approximation

Unified LASSO Estimation by Least Squares Approximation We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least squares problems. Thereafter, the standard asymptotic theory can be established and the LARS algorithm can be applied. In particular, if the adaptive LASSO penalty and a Bayes information criterion–type tuning parameter selector are used, the resulting LSA estimator can be as efficient as the oracle. Extensive numerical studies confirm our theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the American Statistical Association Taylor & Francis

Unified LASSO Estimation by Least Squares Approximation

10 pages

Loading next page...
 
/lp/taylor-francis/unified-lasso-estimation-by-least-squares-approximation-KH0PthpFUj

References (39)

Publisher
Taylor & Francis
Copyright
© American Statistical Association
ISSN
1537-274X
eISSN
0162-1459
DOI
10.1198/016214507000000509
Publisher site
See Article on Publisher Site

Abstract

We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least squares problems. Thereafter, the standard asymptotic theory can be established and the LARS algorithm can be applied. In particular, if the adaptive LASSO penalty and a Bayes information criterion–type tuning parameter selector are used, the resulting LSA estimator can be as efficient as the oracle. Extensive numerical studies confirm our theory.

Journal

Journal of the American Statistical AssociationTaylor & Francis

Published: Sep 1, 2007

Keywords: Adaptive LASSO; Bayes information criterion; LASSO; Least angle regression; Least squares approximation; Microarray data; Oracle Property; Solution path

There are no references for this article.