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Journal Articles Bernoulli Year : 2022

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.
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Dates and versions

hal-03879507 , version 1 (30-11-2022)

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  • HAL Id : hal-03879507 , version 1

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Alexandra Carpentier, Olivier Collier, Laëtitia Comminges, Alexandre B. Tsybakov, Yuhao Wang. Estimation of the ℓ2-norm and testing in sparse linear regression with unknown variance. Bernoulli, 2022, 28 (4). ⟨hal-03879507⟩
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