Convergence of nonparametric functional regression estimates with functional responses

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1373-1391
Journal / PublicationElectronic Journal of Statistics
Publication statusPublished - 2012
Externally publishedYes


We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let (X1,Y1),...,(Xn,Yn) be random elements in F×H where F is a semi-metric space and H is a separable Hilbert space. Based on a recently introduced notion of weak dependence for functional data, we showed the almost sure convergence rates of both the Nadaraya-Watson estimator and the nearest neighbor estimator, in a unified manner. Several factors, including functional nature of the responses, the assumptions on the functional variables using the Orlicz norm and the desired generality on weakly dependent data, make the theoretical investigations more challenging and interesting.

Research Area(s)

  • Bernstein's inequality for martingale differences, Nadaraya-Watson estimate, Nearest neighbor estimate, Nonparametric functional regression, Orlicz norm