English

Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance

Statistics Theory 2020-10-27 v1 Statistics Theory

Abstract

We consider the related problems of estimating the l2l_2-norm and the squared l2l_2-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with l2l_2 separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.

Keywords

Cite

@article{arxiv.2010.13679,
  title  = {Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance},
  author = {Alexandra Carpentier and Olivier Collier and Laetitia Comminges and Alexandre B. Tsybakov and Yuhao Wang},
  journal= {arXiv preprint arXiv:2010.13679},
  year   = {2020}
}
R2 v1 2026-06-23T19:39:30.556Z