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Minimax rate of testing in sparse linear regression

Carpentier, Alexandra; Collier, Olivier; Comminges, Laëtitia; Tsybakov, Alexandre; Wang, Yuhao (2018), Minimax rate of testing in sparse linear regression, Automation and Remote Control, 80, p. 1817–1834. 10.1134/S0005117919100047

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Automation and Remote Control
Volume
80
Published in
Paris
Pages
1817–1834
Publication identifier
Metadata
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Author(s)
Carpentier, Alexandra

Collier, Olivier
Modélisation aléatoire de Paris X [MODAL'X]
Comminges, Laëtitia
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tsybakov, Alexandre
Centre de Recherche en Économie et Statistique [CREST]
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Wang, Yuhao
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.
Subjects / Keywords
signal detection; sparsity; Gaussian sequence model; linear regression