Minimax rate of testing in sparse linear regression
Statistics Theory
2018-10-11 v3 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1804.06494,
title = {Minimax rate of testing in sparse linear regression},
author = {Alexandra Carpentier and Olivier Collier and Laëtitia Comminges and Alexandre B. Tsybakov and Yuhao Wang},
journal= {arXiv preprint arXiv:1804.06494},
year = {2018}
}