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

By Heng Lian. Electronic Journal of Statistics, 2011

76 citations recorded by the source corpus.

: 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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bc14133ea951e8c92434ed0b392424c475437f08

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Nengxiang Ling
2. Philippe Vieu
3. Heng Lian

In Statistics and Probability

1. Nengxiang Ling
2. Philippe Vieu
3. Heng Lian
4. Peter Hall
5. Frédéric Ferraty
6. M. Febrero–Bande
7. H. Muller
8. Antonio Cuevas

Citations in the corpus

• Nonparametric modelling for functional data: selected survey and tracks for future (2018, background): “(see [67,78]) and rates of convergence are stated, while the local linear estimate is studied in [79] and rates of convergence have been obtained (see also [80]), and rates of convergence for a recursive estimate are stated in [81].”