Journal
BERNOULLI
Volume 23, Issue 1, Pages 552-581Publisher
INT STATISTICAL INST
DOI: 10.3150/15-BEJ756
Keywords
multiple linear regression; oracle inequalities; sparse recovery; total variation penalty
Categories
Funding
- Swiss National Science Foundation
- grant Investissements d'Avenir [ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047]
Ask authors/readers for more resources
Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context of multiple linear regression. We show, in particular, that the incorporation of a simple correlation measure into the tuning parameter can lead to a nearly optimal prediction performance of the Lasso even for highly correlated covariates. However, we also reveal that for moderately correlated covariates, the prediction performance of the Lasso can be mediocre irrespective of the choice of the tuning parameter. We finally show that our results also lead to near-optimal rates for the least-squares estimator with total variation penalty.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available