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

Alexandra Carpentier , Olivier Collier , Laëtitia Comminges (1) , Alexandre B. Tsybakov , Yuhao Wang

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-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 $l_2$ separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.

Domaines: Statistiques [math.ST]

Alexandra Carpentier, Olivier Collier, Laëtitia Comminges, Alexandre B. Tsybakov, Yuhao Wang. Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance. Bernoulli, 2022, ⟨10.3150/21-BEJ1436⟩. ⟨hal-03850120⟩