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VOL. 6 | 2010 Hierarchical selection of variables in sparse high-dimensional regression
Peter J. Bickel, Ya’acov Ritov, Alexandre B. Tsybakov

Editor(s) James O. Berger, T. Tony Cai, Iain M. Johnstone

Abstract

We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two assumptions: (i) there exists a sparse representation of the regression function in a suggested basis, (ii) there are no interactions outside of the set of the corresponding main effects. We suggest an hierarchical randomized search procedure for selection of variables and of their interactions. We show that given an initial estimator, an estimator with a similar prediction loss but with a smaller number of non-zero coordinates can be found.

Information

Published: 1 January 2010
First available in Project Euclid: 26 October 2010

MathSciNet: MR2798511

Digital Object Identifier: 10.1214/10-IMSCOLL605

Subjects:
Primary: 60K35 , 62G08
Secondary: 62C20 , 62G05 , 62G20

Keywords: linear models , Model selection , nonparametric statistics

Rights: Copyright © 2010, Institute of Mathematical Statistics

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