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

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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• Higher criticism for detecting sparse heterogeneous mixtures
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• Nonquadratic estimators of a quadratic functional
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Cited by in corpus (1)

• Near-Optimal Procedures for Model Discrimination with Non-Disclosure Properties