M-Estimation for partially functional linear regression model based on splines. Issue 21 (1st November 2016)

• Record Type: Journal Article
• Authors: Zhou, Jianjun; Du, Jiang; Sun, Zhimeng
• Is Part Of: Communications in statistics. Volume 45:Issue 21(2016)
• Page Start: 6436
• Page End: 6446
• Publication Date: 2016-11-01
• Subjects: B-spline -- M-setimator -- Partially functional linear regression; 62G08 -- 62G20; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.921309
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: M-estimation is a widely used technique for robust statistical inference. In this paper, we study robust partially functional linear regression model in which a scale response variable is explained by a function-valued variable and a finite number of real-valued variables. For the estimation of the regression parameters, which include the infinite dimensional function as well as the slope parameters for the real-valued variables, we use polynomial splines to approximate the slop parameter. The estimation procedure is easy to implement, and it is resistant to heavy-tailederrors or outliers in the response. The asymptotic properties of the proposed estimators are established. Finally, we assess the finite sample performance of the proposed method by Monte Carlo simulation studies.