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

Kangning Wang ^[1] ; Lu Lin ^[2]
1. [1] Chongqing University of Arts and Sciences
  
  Chongqing University of Arts and Sciences
  
  China
2. [2] Shandong University
  
  Shandong University
  
  China
Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 26, Nº. 1, 2017, págs. 22-45
Idioma: inglés
DOI: 10.1007/s11749-016-0496-0
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Resumen
- 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.