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On the Rate of Convergence of the Bagged Nearest Neighbor Estimate

Gérard Biau 1 Frédéric Cérou 2 Arnaud Guyader 2, 3, *
* Corresponding author
2 ASPI - Applications of interacting particle systems to statistics
UR1 - Université de Rennes 1, Inria Rennes – Bretagne Atlantique , CNRS - Centre National de la Recherche Scientifique : UMR6074
Abstract : Bagging is a simple way to combine estimates in order to improve their performance. This method, suggested by Breiman in 1996, proceeds by resampling from the original data set, constructing a predictor from each bootstrap sample, and decide by combining. By bagging an $n$-sample, the crude nearest neighbor regression estimate is turned out into a consistent weighted nearest neighbor regression estimate, which is amenable to statistical analysis. Letting the resampling size $k_n$ grows with $n$ in such a manner that $k_n\to \infty$ and $k_n/n\to 0$, it is shown that this estimate achieves optimal rates of convergence, independently from the fact that resampling is done with or without replacement.
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Submitted on : Thursday, February 26, 2009 - 2:40:56 PM
Last modification on : Tuesday, July 13, 2021 - 3:14:10 AM
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  • HAL Id : inria-00363875, version 2

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Gérard Biau, Frédéric Cérou, Arnaud Guyader. On the Rate of Convergence of the Bagged Nearest Neighbor Estimate. [Research Report] RR-6860, INRIA. 2009, pp.28. ⟨inria-00363875v2⟩

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