# Minimax Rate of Testing in Sparse Linear Regression

@article{Carpentier2018MinimaxRO,
title={Minimax Rate of Testing in Sparse Linear Regression},
author={Alexandra Carpentier and Olivier Collier and Laetitia Comminges and A. Tsybakov and Yuhao Wang},
journal={Automation and Remote Control},
year={2018},
volume={80},
pages={1817 - 1834}
}
• Published 17 April 2018
• Mathematics, Computer Science
• Automation and Remote Control
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 (s/n)log(p/s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage…
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