Error bounds for the convex loss Lasso in linear models
Mark Hannay & Pierre-Yves Deléamont
| Résumé |
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. |
| Mots-clés |
Robust Lasso, high dimensions, error bounds, joint scale and location estimation |
| Citation | Hannay, M., & Deléamont, P. Y. (2017). Error bounds for the convex loss Lasso in linear models. Electronic Journal of Statistics, 11(2), 2832-2875. |
| Type | Article de périodique (Anglais) |
| Date de publication | 2017 |
| Nom du périodique | Electronic Journal of Statistics |
| Volume | 11 |
| Numéro | 2 |
| Pages | 2832-2875 |