Minimax rate of testing in sparse linear regression

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Date
2018
Publishing date
04-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01770434
Dewey
Probabilités et mathématiques appliquées
Sujet
signal detection; sparsity; Gaussian sequence model; linear regression
URI
https://basepub.dauphine.fr/handle/123456789/17937
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Author
Carpentier, Alexandra
4067 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
102 Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
2579 Centre de Recherche en Économie et Statistique [CREST]
Wang, Yuhao
Type
Document de travail / Working paper
Item number of pages
17
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.