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Title: Error bounds for the convex loss Lasso in linear models
Authors: Hannay, Mark
Deléamont, Pierre-Yves
Keywords: Robust Lasso
High Dimensions
Issue Date: 2017
Source: Hannay, M., & Deléamont, P. Y. (2017). Error bounds for the convex loss Lasso in linear models. Electronic Journal of Statistics, 11(2), 2832-2875. doi:10.1214/17-EJS1304
Series/Report no.: Electronic Journal of Statistics
Abstract: 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.
DOI: 10.1214/17-EJS1304
Rights: © 2017 © The Author(s) (published by The Institute of Mathematical Statistics and The Bernoulli Society for Mathematical Statistics and Probability). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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