Estimation of the ℓ2-norm and testing in sparse linear regression with unknown variance-Reference-Cited by-同舟云学术

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

Published:2022-11-01 Issue:4 Volume:28 Page:
ISSN:1350-7265
Container-title:Bernoulli
language:
Short-container-title:Bernoulli

Author:

Carpentier Alexandra¹,Collier Olivier²,Comminges Laetitia³,Tsybakov Alexandre B.⁴,Wang Yuhao⁵

Affiliation:

1. Institut für Mathematik, Universität Potsdam, Potsdam, Germany

2. Modal’X, Université Paris-Nanterre, Nanterre and CREST, Paris, France

3. CEREMADE, Université Paris-Dauphine and CREST, Paris, France

4. CREST, ENSAE and Institut Polytechnique de Paris, Paris, France

5. Tsinghua University, Beijing, China and Shanghai Qi Zhi Institute, Shanghai, China

Publisher

Bernoulli Society for Mathematical Statistics and Probability

Subject

Statistics and Probability

Reference27 articles.

1. Vershynin, R. (2018). High-Dimensional Probability: An Introduction with Applications in Data Science. Cambridge Series in Statistical and Probabilistic Mathematics 47. Cambridge: Cambridge Univ. Press. 10.1017/9781108231596

2. Tsybakov, A.B. (2009). Introduction to Nonparametric Estimation. Springer Series in Statistics. New York: Springer. 10.1007/b13794

3. Adamczak, R. and Wolff, P. (2015). Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order. Probab. Theory Related Fields 162 531–586. 10.1007/s00440-014-0579-3

4. Arias-Castro, E., Candès, E.J. and Plan, Y. (2011). Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism. Ann. Statist. 39 2533–2556. 10.1214/11-AOS910

5. Bellec, P.C., Lecué, G. and Tsybakov, A.B. (2018). Slope meets Lasso: Improved oracle bounds and optimality. Ann. Statist. 46 3603–3642. 10.1214/17-AOS1670

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