Asymptotic normality of locally modelled regression estimator for functional data |
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Authors: | Zhiyong Zhou Zhengyan Lin |
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Institution: | Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China |
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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. |
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Keywords: | functional data locally modelled regression asymptotic normality empirical likelihood |
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