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This article is cited in 7 scientific papers (total in 7 papers)
Minimax rate of testing in sparse linear regression
A. Carpentiera, O. Collierbc, L. Commingescd, A. B. Tsybakove, Yu. Wangf a University of Magdeburg, Magdeburg, Germany
b Modal'X, Université Paris-Nanterre, Paris, France
c CREST, Paris, France
d CEREMADE, Université Paris-Dauphine, Paris, France
e CREST, ENSAE, Paris, France
f LIDS-IDSS, MIT, Cambridge, USA
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 $\ell_2$-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 $\ell_2$-norm of the regression parameter.
Keywords:
linear regression, sparsity, signal detection.
Received: 19.07.2018 Revised: 03.10.2018 Accepted: 08.11.2018
Citation:
A. Carpentier, O. Collier, L. Comminges, A. B. Tsybakov, Yu. Wang, “Minimax rate of testing in sparse linear regression”, Avtomat. i Telemekh., 2019, no. 10, 78–99; Autom. Remote Control, 80:10 (2019), 1817–1834
Linking options:
https://www.mathnet.ru/eng/at15365 https://www.mathnet.ru/eng/at/y2019/i10/p78
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Abstract page: | 169 | Full-text PDF : | 27 | References: | 19 | First page: | 6 |
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