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On the local linear estimate for functional regression: Uniform in bandwidth consistency
Journal article   Peer reviewed

On the local linear estimate for functional regression: Uniform in bandwidth consistency

Mohammed Attouch, Ali Laksaci and Fatima Rafaa
Communications in statistics. Theory and methods, Vol.48(8), pp.1836-1853
18/04/2019
DOI: https://doi.org/10.1080/03610926.2018.1440308

Abstract

Almost complete consistency Bandwidth parameter Functional data analysis Functional local linear regression UIB consistency
We consider the problem of local linear estimation of the regression function when the regressor is functional. The main result of this paper is to prove the strong convergence (with rates), uniformly in bandwidth parameters (UIB), of the considered estimator. The main interest of this result is the possibility to derive the asymptotic properties of our estimate even if the bandwidth parameter is a random variable.

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