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arXiv · 2010.13679

Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance

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

We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-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 $l_2$ separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.

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Alexandra Carpentier, Olivier Collier, Laetitia Comminges, Alexandre B. Tsybakov, Yuhao Wang. 2020-10-26. Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance. https://arxiv.org/abs/2010.13679

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