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

2020/10/26 by Alexandra Carpentier, Carpentier, Alexandra, Olivier Collier +7 · 1 citation
Engineering · Mathematics · #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2010.13679

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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