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December 2016 On marginal sliced inverse regression for ultrahigh dimensional model-free feature selection
Zhou Yu, Yuexiao Dong, Jun Shao
Ann. Statist. 44(6): 2594-2623 (December 2016). DOI: 10.1214/15-AOS1424

Abstract

Model-free variable selection has been implemented under the sufficient dimension reduction framework since the seminal paper of Cook [Ann. Statist. 32 (2004) 1062–1092]. In this paper, we extend the marginal coordinate test for sliced inverse regression (SIR) in Cook (2004) and propose a novel marginal SIR utility for the purpose of ultrahigh dimensional feature selection. Two distinct procedures, Dantzig selector and sparse precision matrix estimation, are incorporated to get two versions of sample level marginal SIR utilities. Both procedures lead to model-free variable selection consistency with predictor dimensionality $p$ diverging at an exponential rate of the sample size $n$. As a special case of marginal SIR, we ignore the correlation among the predictors and propose marginal independence SIR. Marginal independence SIR is closely related to many existing independence screening procedures in the literature, and achieves model-free screening consistency in the ultrahigh dimensional setting. The finite sample performances of the proposed procedures are studied through synthetic examples and an application to the small round blue cell tumors data.

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Zhou Yu. Yuexiao Dong. Jun Shao. "On marginal sliced inverse regression for ultrahigh dimensional model-free feature selection." Ann. Statist. 44 (6) 2594 - 2623, December 2016. https://doi.org/10.1214/15-AOS1424

Information

Received: 1 May 2015; Revised: 1 December 2015; Published: December 2016
First available in Project Euclid: 23 November 2016

zbMATH: 1359.62218
MathSciNet: MR3576555
Digital Object Identifier: 10.1214/15-AOS1424

Subjects:
Primary: 62G99 , 62H20 , 62H99

Keywords: Marginal coordinate test , sliced inverse regression , sufficient dimension reduction , sure independence screening

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 6 • December 2016
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