Estimation of the ℓ2-norm and testing in sparse linear regression with unknown variance

Alexandra Carpentier; Olivier Collier; Laetitia Comminges; Alexandre B. Tsybakov; Yuhao Wang

doi:10.3150/21-BEJ1436

Estimation of the ℓ₂-norm and testing in sparse linear regression with unknown variance

Alexandra Carpentier
, Olivier Collier
, Laetitia Comminges
, Alexandre B. Tsybakov
, Yuhao Wang

Institut für Mathematik der Universität Potsdam
Université Paris-Nanterre
Université Paris Dauphine
ENSAE
Tsinghua University
Shanghai Qi Zhi Institute

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the related problems of estimating the ℓ₂-norm and the squared ℓ₂-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with ℓ₂ separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.

Original language	English
Pages (from-to)	2788-2787
Number of pages	2
Journal	Bernoulli
Volume	28
Issue number	4
DOIs	https://doi.org/10.3150/21-BEJ1436
Publication status	Published - 1 Nov 2022
Externally published	Yes

Keywords

Sparse linear regression
non-linear functional estimation
signal detection

Access to Document

10.3150/21-BEJ1436

Cite this

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title = "Estimation of the ℓ2-norm and testing in sparse linear regression with unknown variance",

abstract = "We consider the related problems of estimating the ℓ2-norm and the squared ℓ2-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with ℓ2 separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.",

keywords = "Sparse linear regression, non-linear functional estimation, signal detection",

author = "Alexandra Carpentier and Olivier Collier and Laetitia Comminges and Tsybakov, \{Alexandre B.\} and Yuhao Wang",

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AU - Collier, Olivier

AU - Comminges, Laetitia

AU - Tsybakov, Alexandre B.

AU - Wang, Yuhao

PY - 2022/11/1

Y1 - 2022/11/1

N2 - We consider the related problems of estimating the ℓ2-norm and the squared ℓ2-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with ℓ2 separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.

AB - We consider the related problems of estimating the ℓ2-norm and the squared ℓ2-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with ℓ2 separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.

KW - Sparse linear regression

KW - non-linear functional estimation

KW - signal detection

U2 - 10.3150/21-BEJ1436

DO - 10.3150/21-BEJ1436

M3 - Article

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SN - 1350-7265

VL - 28

SP - 2788

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JO - Bernoulli

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