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Automation and Remote Control

, Volume 80, Issue 10, pp 1817–1834 | Cite as

Minimax Rate of Testing in Sparse Linear Regression

  • A. CarpentierEmail author
  • O. Collier
  • L. Comminges
  • A. B. Tsybakov
  • Yu. Wang
Topical Issue
  • 14 Downloads

Abstract

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 l2-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 \(\sqrt {\left( {s/n} \right)\log \left( {\sqrt p /s} \right)}\). We also show that this is the minimax rate of estimation of the l2-norm of the regression parameter.

Keywords

linear regression sparsity signal detection 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • A. Carpentier
    • 1
    Email author
  • O. Collier
    • 2
  • L. Comminges
    • 3
  • A. B. Tsybakov
    • 4
  • Yu. Wang
    • 5
  1. 1.University of MagdeburgMagdeburgGermany
  2. 2.Modal’X, Université Paris-Nanterre è CRESTParisFrance
  3. 3.CEREMADE, Université Paris-Dauphine è CRESTParisFrance
  4. 4.CREST, ENSAEParisFrance
  5. 5.LIDS-IDSS, MITCambridgeUSA

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