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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