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 -norm and the squared -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 separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.
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}
}