Open Access
February 2015 Variable selection and estimation for semi-parametric multiple-index models
Tao Wang, Peirong Xu, Lixing Zhu
Bernoulli 21(1): 242-275 (February 2015). DOI: 10.3150/13-BEJ566


In this paper, we propose a novel method to select significant variables and estimate the corresponding coefficients in multiple-index models with a group structure. All existing approaches for single-index models cannot be extended directly to handle this issue with several indices. This method integrates a popularly used shrinkage penalty such as LASSO with the group-wise minimum average variance estimation. It is capable of simultaneous dimension reduction and variable selection, while incorporating the group structure in predictors. Interestingly, the proposed estimator with the LASSO penalty then behaves like an estimator with an adaptive LASSO penalty. The estimator achieves consistency of variable selection without sacrificing the root-$n$ consistency of basis estimation. Simulation studies and a real-data example illustrate the effectiveness and efficiency of the new method.


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Tao Wang. Peirong Xu. Lixing Zhu. "Variable selection and estimation for semi-parametric multiple-index models." Bernoulli 21 (1) 242 - 275, February 2015.


Published: February 2015
First available in Project Euclid: 17 March 2015

zbMATH: 06436793
MathSciNet: MR3322318
Digital Object Identifier: 10.3150/13-BEJ566

Keywords: Adaptive LASSO , group-wise dimension reduction , minimum average variance estimation , mixed-rates asymptotics , model-free variable selection , sufficient dimension reduction

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 1 • February 2015
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