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Asymptotic normality of locally modelled regression estimator for functional data
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China.
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China.
2016 (English)In: Journal of nonparametric statistics (Print), ISSN 1048-5252, E-ISSN 1029-0311, Vol. 28, no 1, p. 116-131Article in journal (Refereed) Published
Abstract [en]

We focus on the nonparametric regression of a scalar response on a functional explanatory variable. As analternative to the well-known Nadaraya-Watson estimator for regression function in this framework, thelocally 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 functionaldata are considered. The mean-squared convergence as well as asymptotic normality for the estimator areestablished. We also adapt the empirical likelihood method to construct the point-wise confidence intervalsfor 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.

Place, publisher, year, edition, pages
2016. Vol. 28, no 1, p. 116-131
Keywords [en]
functional data, locally modelled regression, asymptotic normality, empirical likelihood
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-127063DOI: 10.1080/10485252.2015.1114112OAI: oai:DiVA.org:umu-127063DiVA, id: diva2:1040544
Available from: 2016-10-27 Created: 2016-10-27 Last updated: 2018-11-14Bibliographically approved

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Zhou, Zhiyong

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