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Robust and efficient direction identification for groupwise additive multiple-index models and its applications

Kangning Wang () and Lu Lin ()
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Kangning Wang: Shandong Technology and Business University
Lu Lin: Shandong University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 26, issue 1, 22-45

Abstract: Abstract This paper concerns robust and efficient direction identification for a groupwise additive multiple-index model, in which each additive function has a single-index structure. Interestingly, without involving non-parametric approach, we show that the directions of all the index parameter vectors can be recovered by a simple linear composite quantile regression (CQR). As a specific application, a iterative-free CQR estimation procedure for the partially linear single-index model is proposed. Furthermore, it can also be used to develop a penalized CQR procedure for variable selection in the high-dimensional settings. The new method has superiority in robustness and efficiency by inheriting the advantage of the CQR approach. Simulation results and real-data analysis also confirm our method.

Keywords: Robust; Variable selection; High dimensionality; Index estimation; Multiple-index models; 62G05; 62E20; 62J02 (search for similar items in EconPapers)
Date: 2017
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