Open Access
VOL. 3 | 2008 Consistent selection via the Lasso for high dimensional approximating regression models
Florentina Bunea

Editor(s) Bertrand Clarke, Subhashis Ghosal

Inst. Math. Stat. (IMS) Collect., 2008: 122-137 (2008) DOI: 10.1214/074921708000000101


In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function f with elements of a given dictionary of M functions. The target for consistency is the index set of those functions from this dictionary that realize the most parsimonious approximation to f among all linear combinations belonging to an L2 ball centered at f and of radius r2n, M. In this framework we show that a consistent estimate of this index set can be derived via 1 penalized least squares, with a data dependent penalty and with tuning sequence rn, M>$\sqrt{\log(Mn)/n}$, where n is the sample size. Our results hold for any 1≤Mnγ, for any γ>0.


Published: 1 January 2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2459221

Digital Object Identifier: 10.1214/074921708000000101

Primary: 62G08
Secondary: 62C20 , 62G05 , 62G20

Keywords: consistency , high dimension , L_1 regularization , Lasso , Penalty , regression , selection

Rights: Copyright © 2008, Institute of Mathematical Statistics

Back to Top