Minimax rate of testing in sparse linear regression

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Date
2018
Publisher city
Paris
Dewey
Probabilités et mathématiques appliquées
Sujet
signal detection; sparsity; Gaussian sequence model; linear regression
Journal issue
Automation and Remote Control
Volume
80
Publication date
2018
Article pages
1817–1834
DOI
http://dx.doi.org/10.1134/S0005117919100047
URI
https://basepub.dauphine.fr/handle/123456789/17937
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Author
Carpentier, Alexandra
120520 Statistical Laboratory [DPMMS]
Collier, Olivier
101 Modélisation aléatoire de Paris X [MODAL'X]
Comminges, Laëtitia
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tsybakov, Alexandre
2579 Centre de Recherche en Économie et Statistique [CREST]
102 Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Wang, Yuhao
543049 Nanyang Technological University, Energy Research Institute at NTU (ERIAN)
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider the problem of testing the hypothesis that the parameter of linear regression model is 0 against an s-sparse alternative separated from 0 in the 2-distance. We show that, in Gaussian linear regression model with p < n, where p is the dimension of the parameter and n is the sample size, the non-asymptotic minimax rate of testing has the form sqrt((s/n) log(1 + sqrt(p)/s)). We also show that this is the minimax rate of estimation of the 2-norm of the regression parameter. MSC 2010 subject classifications: 62J05, 62G10.