Electronic Journal of Statistics

Convergence of functional k-nearest neighbor regression estimate with functional responses

Heng Lian

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Abstract

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.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 31-40.

Dates
First available in Project Euclid: 7 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1297088517

Digital Object Identifier
doi:10.1214/11-EJS595

Mathematical Reviews number (MathSciNet)
MR2773606

Zentralblatt MATH identifier
1274.62291

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Keywords
Functional response models martingale difference sequence nearest neighbor estimate rates of convergence

Citation

Lian, Heng. Convergence of functional k-nearest neighbor regression estimate with functional responses. Electron. J. Statist. 5 (2011), 31--40. doi:10.1214/11-EJS595. https://projecteuclid.org/euclid.ejs/1297088517


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