Asymptotic normality of locally modelled regression estimator for functional data

Zhiyong Zhou and Zhengyan Lin

Journal of Nonparametric Statistics, 2016, vol. 28, issue 1, 116-131

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.

Date: 2016
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Citations: View citations in EconPapers (6)

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DOI: 10.1080/10485252.2015.1114112

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