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Minimax rate of testing in sparse linear regression

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 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.
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Contributor : Olivier Collier <>
Submitted on : Thursday, April 19, 2018 - 8:16:57 AM
Last modification on : Friday, March 27, 2020 - 3:24:53 AM
Document(s) archivé(s) le : Tuesday, September 18, 2018 - 11:36:41 AM


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  • HAL Id : hal-01770434, version 1


Alexandra Carpentier, Olivier Collier, Laëtitia Comminges, Alexandre Tsybakov, Yuhao Wang. Minimax rate of testing in sparse linear regression. 2018. ⟨hal-01770434⟩



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