Open Access
Translator Disclaimer
2017 Error bounds for the convex loss Lasso in linear models
Mark Hannay, Pierre-Yves Deléamont
Electron. J. Statist. 11(2): 2832-2875 (2017). DOI: 10.1214/17-EJS1304


In this paper we investigate error bounds for convex loss functions for the Lasso in linear models, by first establishing a gap in the theory with respect to the existing error bounds. Then, under the compatibility condition, we recover bounds for the absolute value estimation error and the squared prediction error under mild conditions, which appear to be far more appropriate than the existing bounds for the convex loss Lasso. Interestingly, asymptotically the only difference between the new bounds of the convex loss Lasso and the classical Lasso is a term solely depending on a well-known expression in the robust statistics literature appearing multiplicatively in the bounds. We show that this result holds whether or not the scale parameter needs to be estimated jointly with the regression coefficients. Finally, we use the ratio to optimize our bounds in terms of minimaxity.


Download Citation

Mark Hannay. Pierre-Yves Deléamont. "Error bounds for the convex loss Lasso in linear models." Electron. J. Statist. 11 (2) 2832 - 2875, 2017.


Received: 1 January 2017; Published: 2017
First available in Project Euclid: 8 August 2017

zbMATH: 1373.62369
MathSciNet: MR3694570
Digital Object Identifier: 10.1214/17-EJS1304

Primary: 62F35
Secondary: 62J07

Keywords: error bounds , high dimensions , joint scale and location estimation , Robust Lasso


Vol.11 • No. 2 • 2017
Back to Top