Convergence of functional k-nearest neighbor regression estimate 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)31-40
Journal / PublicationElectronic Journal of Statistics
Publication statusPublished - 2011
Externally publishedYes


Let (X 1, Y 1),..., (X n, Y n) be independent and identically dis-tributed random elements taking values in F×H, where F is a semi-metric space and H is a separable Hilbert space. We investigate the rates of strong (almost sure) convergence of the k-nearest neighbor estimate. We give two convergence results assuming a finite moment condition and exponential tail condition on the noises respectively, with the latter requiring less stringent conditions on k for convergence.

Research Area(s)

  • Functional response models, Martingale difference sequence, Nearest neighbor estimate, Rates of convergence