Minimax rate of testing in sparse linear regression

2018/04/17 by Alexandra Carpentier, Carpentier, Alexandra, Olivier Collier +7 · 1 citation
Engineering · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1804.06494

openalex publication_date 2018/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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