Open Access
2011 Convergence of functional k-nearest neighbor regression estimate with functional responses
Heng Lian
Electron. J. Statist. 5: 31-40 (2011). DOI: 10.1214/11-EJS595


Let (X1,Y1),,(Xn,Yn) be independent and identically distributed 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.


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Heng Lian. "Convergence of functional k-nearest neighbor regression estimate with functional responses." Electron. J. Statist. 5 31 - 40, 2011.


Published: 2011
First available in Project Euclid: 7 February 2011

zbMATH: 1274.62291
MathSciNet: MR2773606
Digital Object Identifier: 10.1214/11-EJS595

Primary: 62G08
Secondary: 62G20

Keywords: Functional response models , Martingale difference sequence , nearest neighbor estimate , rates of convergence

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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