English

A note on sharp oracle bounds for Slope and Lasso

Statistics Theory 2021-07-26 v1 Statistics Theory

Abstract

In this paper, we study the sharp oracle bounds for Slope and Lasso and generalize the results in Bellec et al. (2018) to allow the case that the parameter vector is not exactly sparse and obtain the optimal bounds for q\ell_q estimation errors with 1q1\leq q\leq \infty by using some extended Restricted Eigenvalue type conditions.

Cite

@article{arxiv.2107.10974,
  title  = {A note on sharp oracle bounds for Slope and Lasso},
  author = {Zhiyong Zhou},
  journal= {arXiv preprint arXiv:2107.10974},
  year   = {2021}
}
R2 v1 2026-06-24T04:26:55.358Z