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August 2015 The fused Kolmogorov filter: A nonparametric model-free screening method
Qing Mai, Hui Zou
Ann. Statist. 43(4): 1471-1497 (August 2015). DOI: 10.1214/14-AOS1303

Abstract

A new model-free screening method called the fused Kolmogorov filter is proposed for high-dimensional data analysis. This new method is fully nonparametric and can work with many types of covariates and response variables, including continuous, discrete and categorical variables. We apply the fused Kolmogorov filter to deal with variable screening problems emerging from a wide range of applications, such as multiclass classification, nonparametric regression and Poisson regression, among others. It is shown that the fused Kolmogorov filter enjoys the sure screening property under weak regularity conditions that are much milder than those required for many existing nonparametric screening methods. In particular, the fused Kolmogorov filter can still be powerful when covariates are strongly dependent on each other. We further demonstrate the superior performance of the fused Kolmogorov filter over existing screening methods by simulations and real data examples.

Citation

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Qing Mai. Hui Zou. "The fused Kolmogorov filter: A nonparametric model-free screening method." Ann. Statist. 43 (4) 1471 - 1497, August 2015. https://doi.org/10.1214/14-AOS1303

Information

Received: 1 October 2014; Published: August 2015
First available in Project Euclid: 17 June 2015

zbMATH: 06470427
MathSciNet: MR3357868
Digital Object Identifier: 10.1214/14-AOS1303

Subjects:
Primary: 62G99

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 4 • August 2015
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