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| HAL: inria-00363875, version 2 |
| See detailed view |  BibTeX,EndNote,... |
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| Available versions | v1 (2009-02-24) | v2 (2009-02-27) |
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| On the Rate of Convergence of the Bagged Nearest Neighbor Estimate |
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| Gérard Biau 1Frédéric Cérou 2 |
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| (2009) |
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| 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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| 1: | Laboratoire de Statistique Théorique et Appliquée (LSTA) |
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Université Pierre et Marie Curie (UPMC) - Paris VI |
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| 2: | ASPI (INRIA - IRISA) |
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CNRS : UMR6074 – INRIA – Université de Rennes 1 |
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| 3: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Domain | : | Mathematics/Statistics Statistics/Statistics Theory |
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| Bagging – Resampling – Nearest neighbors – Rates of convergence. |
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| inria-00363875, version 2 | |
| http://hal.inria.fr/inria-00363875 | |
| oai:hal.inria.fr:inria-00363875 | |
| From: Arnaud Guyader | |
| Submitted on: Thursday, 26 February 2009 14:40:56 | |
| Updated on: Monday, 22 March 2010 13:43:44 | |
