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August 2013 Marginal empirical likelihood and sure independence feature screening
Jinyuan Chang, Cheng Yong Tang, Yichao Wu
Ann. Statist. 41(4): 2123-2148 (August 2013). DOI: 10.1214/13-AOS1139

Abstract

We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening procedure for linear models and the generalized linear models. Different from most existing feature screening approaches that rely on the magnitudes of some marginal estimators to identify true signals, the proposed screening approach is capable of further incorporating the level of uncertainties of such estimators. Such a merit inherits the self-studentization property of the empirical likelihood approach, and extends the insights of existing feature screening methods. Moreover, we show that our screening approach is less restrictive to distributional assumptions, and can be conveniently adapted to be applied in a broad range of scenarios such as models specified using general moment conditions. Our theoretical results and extensive numerical examples by simulations and data analysis demonstrate the merits of the marginal empirical likelihood approach.

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Jinyuan Chang. Cheng Yong Tang. Yichao Wu. "Marginal empirical likelihood and sure independence feature screening." Ann. Statist. 41 (4) 2123 - 2148, August 2013. https://doi.org/10.1214/13-AOS1139

Information

Published: August 2013
First available in Project Euclid: 23 October 2013

zbMATH: 1277.62109
MathSciNet: MR3127860
Digital Object Identifier: 10.1214/13-AOS1139

Subjects:
Primary: 62G09
Secondary: 62H99

Keywords: empirical likelihood , high-dimensional data analysis , large deviation , sure independence screening

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 4 • August 2013
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