Minimax Rate of Testing in Sparse Linear Regression
Minimax Rate of Testing in Sparse Linear Regression
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稀疏线性回归中的极小极大测试率
DOI：
10.1134/s0005117919100047
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发表时间：
2018
影响因子：
0.7
通讯作者：
Yuhao Wang
中科院分区：
文献类型：
--
作者：
A. Carpentier;O. Collier;L. Comminges;A. Tsybakov;Yuhao Wang
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{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt {\left( {s/n} \right)\log \left( {\sqrt p /s} \right)}$$\end{document}. We also show that this is the minimax rate of estimation of the l2-norm of the regression parameter.
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{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt {\left( {s/n} \right)\log \left( {\sqrt p /s} \right)}$$\end{document}. We also show that this is the minimax rate of estimation of the l2-norm of the regression parameter.