Robust estimation and variable selection for varying-coefficient single-index models based on modal regression. Issue 14 (17th July 2016)

• Record Type: Journal Article
• Authors: Yang, Hu; Lv, Jing; Guo, Chaohui
• Is Part Of: Communications in statistics. Volume 45:Issue 14(2016)
• Page Start: 4048
• Page End: 4067
• Publication Date: 2016-07-17
• Subjects: B-spline -- Modal regression -- Oracle property -- Robust estimation -- Varying-coefficient single-index model; Primary: 62G05 -- Secondary: 62G20; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.915043
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this paper, we propose a new efficient and robust penalized estimating procedure for varying-coefficient single-index models based on modal regression and basis function approximations. The proposed procedure simultaneously solves two types of problems: separation of varying and constant effects and selection of variables with non zero coefficients for both non parametric and index components using three smoothly clipped absolute deviation (SCAD) penalties. With appropriate selection of the tuning parameters, the new method possesses the consistency in variable selection and the separation of varying and constant coefficients. In addition, the estimators of varying coefficients possess the optimal convergence rate and the estimators of constant coefficients and index parameters have the oracle property. Finally, we investigate the finite sample performance of the proposed method through a simulation study and real data analysis.