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April 2016 Local independence feature screening for nonparametric and semiparametric models by marginal empirical likelihood
Jinyuan Chang, Cheng Yong Tang, Yichao Wu
Ann. Statist. 44(2): 515-539 (April 2016). DOI: 10.1214/15-AOS1374

Abstract

We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in conjunction with marginal nonparametric regressions. Since our approach actually requires no estimation, it is advantageous in scenarios such as the single-index models where even specification and identification of a marginal model is an issue. By automatically incorporating the level of variation of the nonparametric regression and directly assessing the strength of data evidence supporting local contribution from each explanatory variable, our approach provides a unique perspective for solving feature screening problems. Theoretical analysis shows that our approach can handle data dimensionality growing exponentially with the sample size. With extensive theoretical illustrations and numerical examples, we show that the local independence screening approach performs promisingly.

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Jinyuan Chang. Cheng Yong Tang. Yichao Wu. "Local independence feature screening for nonparametric and semiparametric models by marginal empirical likelihood." Ann. Statist. 44 (2) 515 - 539, April 2016. https://doi.org/10.1214/15-AOS1374

Information

Received: 1 February 2015; Revised: 1 August 2015; Published: April 2016
First available in Project Euclid: 17 March 2016

zbMATH: 06579666
MathSciNet: MR3476608
Digital Object Identifier: 10.1214/15-AOS1374

Subjects:
Primary: 62G99
Secondary: 62H99

Keywords: empirical likelihood , high-dimensional data analysis , nonparametric and semiparametric models , sure independence screening

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 2 • April 2016
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