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June 2014 On asymptotically optimal confidence regions and tests for high-dimensional models
Sara van de Geer, Peter Bühlmann, Ya’acov Ritov, Ruben Dezeure
Ann. Statist. 42(3): 1166-1202 (June 2014). DOI: 10.1214/14-AOS1221


We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking dependence among tests into account. For linear models, our method is essentially the same as in Zhang and Zhang [J. R. Stat. Soc. Ser. B Stat. Methodol. 76 (2014) 217–242]: we analyze its asymptotic properties and establish its asymptotic optimality in terms of semiparametric efficiency. Our method naturally extends to generalized linear models with convex loss functions. We develop the corresponding theory which includes a careful analysis for Gaussian, sub-Gaussian and bounded correlated designs.


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Sara van de Geer. Peter Bühlmann. Ya’acov Ritov. Ruben Dezeure. "On asymptotically optimal confidence regions and tests for high-dimensional models." Ann. Statist. 42 (3) 1166 - 1202, June 2014.


Published: June 2014
First available in Project Euclid: 20 June 2014

zbMATH: 1305.62259
MathSciNet: MR3224285
Digital Object Identifier: 10.1214/14-AOS1221

Primary: 62J07
Secondary: 62F25 , 62J12

Keywords: central limit theorem , generalized linear model , Lasso , linear model , multiple testing , Semiparametric efficiency , Sparsity

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 3 • June 2014
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