Estimation of the l2-norm and testing in sparse linear regression with unknown variance

被引：4

作者：

Carpentier, Alexandra ^{[1
]}

Collier, Olivier ^{[2
,3
]}

Comminges, Laetitia ^{[3
,4
]}

Tsybakov, Alexandre B. ^{[5
,6
]}

Wang, Yuhao ^{[7
,8
]}

机构：

[1] Univ Potsdam, Inst Math, Potsdam, Germany

[2] Univ Paris Nanterre, ModalX, Paris, France

[3] CREST, Paris, France

[4] Univ Paris 09, CEREMADE, Paris, France

[5] ENSAE, CREST, Paris, France

[6] Inst Polytech Paris, Paris, France

[7] Tsinghua Univ, Beijing, Peoples R China

[8] Shanghai Qi Zhi Inst, Shanghai, Peoples R China

来源：

BERNOULLI | 2022年 / 28卷 / 04期

关键词：

Sparse linear regression; signal detection; non-linear functional estimation; ADAPTIVE ESTIMATION; FUNCTIONALS; BOUNDS; LASSO;

D O I：

10.3150/21-BEJ1436

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the related problems of estimating the l(2)-norm and the squared l(2)-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with l(2) separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.

引用

页码：2744 / 2787

页数：44

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