Robust variable selection and parametric component identification in varying coefficient models. Issue 18 (16th September 2016)

• Record Type: Journal Article
• Authors: Yang, Hu; Lv, Jing; Guo, Chaohui
• Is Part Of: Communications in statistics. Volume 45:Issue 18(2016)
• Page Start: 5533
• Page End: 5549
• Publication Date: 2016-09-16
• Subjects: B-spline -- Group variable selection -- Rank-based analysis -- SCAD -- Separation of varying and constant effects; Primary 62G05 -- Secondary 62G20; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.948199
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this paper, we study a novelly robust variable selection and parametric component identification simultaneously in varying coefficient models. The proposed estimator is based on spline approximation and two smoothly clipped absolute deviation (SCAD) penalties through rank regression, which is robust with respect to heavy-tailed errors or outliers in the response. Furthermore, when the tuning parameter is chosen by modified BIC criterion, we show that the proposed procedure is consistent both in variable selection and the separation of varying and constant coefficients. In addition, the estimators of varying coefficients possess the optimal convergence rate under some assumptions, and the estimators of constant coefficients have the same asymptotic distribution as their counterparts obtained when the true model is known. Simulation studies and a real data example are undertaken to assess the finite sample performance of the proposed variable selection procedure.