Thumbnail

Estimation of the ℓ2-norm and testing in sparse linear regression with unknown variance

Carpentier, Alexandra; Collier, Olivier; Comminges, Laëtitia; Tsybakov, Alexandre B.; Wang, Y. (2022), Estimation of the ℓ2-norm and testing in sparse linear regression with unknown variance, Bernoulli, 28, 4, p. 2744-2787. 10.3150/21-BEJ1436

View/Open
Type
Article accepté pour publication ou publié
Date
2022
Journal name
Bernoulli
Volume
28
Number
4
Publisher
International Statistical Institute
Pages
2744-2787
Publication identifier
Metadata
Show full item record
Author(s)
Carpentier, Alexandra
Institut für Mathematik [Potsdam]
Collier, Olivier
Modélisation aléatoire de Paris X [MODAL'X]
Comminges, Laëtitia
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tsybakov, Alexandre B.
Centre de Recherche en Économie et Statistique [CREST]
Wang, Y.
Abstract (EN)
We consider the related problems of estimating the ℓ2-norm and the squared ℓ2-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 ℓ2 separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.
Subjects / Keywords
non-linear functional estimation; signal detection; sparse linear regression