Marginal empirical likelihood and sure independence feature screening

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.

Published in at http://dx.doi.org/10.1214/13-AOS1139 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Asymptotic properties of bridge estimators in sparse high-dimensional regression models
• Extending the scope of empirical likelihood
• A test for model specification of diffusion processes
• High dimensional generalized empirical likelihood for moment restrictions with dependent data

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• Cramér-type moderate deviations for Studentized two-sample $U$-statistics with applications
• High-dimensional empirical likelihood inference
• Testing the martingale difference hypothesis in high dimension
• Variable Screening for High Dimensional Time Series
• Optimal covariance matrix estimation for high-dimensional noise in high-frequency data
• Nonparametric Independence Screening via Favored Smoothing Bandwidth
• Nonparametric Screening under Conditional Strictly Convex Loss for Ultrahigh Dimensional Sparse Data