Asymptotic normality of locally modelled regression estimator for functional data. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Zhou, Zhiyong; Lin, Zhengyan
• Is Part Of: Journal of nonparametric statistics. Volume 28:Issue 1(2016)
• Page Start: 116
• Page End: 131
• Publication Date: 2016-01-02
• Subjects: functional data -- locally modelled regression -- asymptotic normality -- empirical likelihood; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2015.1114112
• Languages: English
• ISSNs: 1048-5252

Abstract

Abstract : We focus on the nonparametric regression of a scalar response on a functional explanatory variable. As an alternative to the well-known Nadaraya-Watson estimator for regression function in this framework, the locally modelled regression estimator performs very well [cf. [Barrientos-Marin, J., Ferraty, F., and Vieu, P. (2010), 'Locally Modelled Regression and Functional Data', Journal of Nonparametric Statistics, 22, 617–632]. In this paper, the asymptotic properties of locally modelled regression estimator for functional data are considered. The mean-squared convergence as well as asymptotic normality for the estimator are established. We also adapt the empirical likelihood method to construct the point-wise confidence intervals for the regression function and derive the Wilk's phenomenon for the empirical likelihood inference. Furthermore, a simulation study is presented to illustrate our theoretical results.