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arXiv · 1804.06494

Minimax rate of testing in sparse linear regression

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

We consider the problem of testing the hypothesis that the parameter of linear regression model is 0 against an s-sparse alternative separated from 0 in the l2-distance. We show that, in Gaussian linear regression model with p < n, where p is the dimension of the parameter and n is the sample size, the non-asymptotic minimax rate of testing has the form sqrt((s/n) log(1 + sqrt(p)/s )). We also show that this is the minimax rate of estimation of the l2-norm of the regression parameter.

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Alexandra Carpentier, Olivier Collier, Laëtitia Comminges, Alexandre B. Tsybakov, Yuhao Wang. 2018-04-17. Minimax rate of testing in sparse linear regression. https://arxiv.org/abs/1804.06494

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