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 HAL: inria-00363875, version 2
 Available versions v1 (2009-02-24) v2 (2009-02-27)
 On the Rate of Convergence of the Bagged Nearest Neighbor Estimate
 Gérard Biau 1, Frédéric Cérou 2, Arnaud Guyader ( ) 2, 3
 (2009)
 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.
 1: Laboratoire de Statistique Théorique et Appliquée (LSTA) Université Pierre et Marie Curie [UPMC] - Paris VI 2: ASPI (INRIA - IRISA) CNRS : UMR6074 – INRIA – Université de Rennes 1 3: Institut de Recherche Mathématique de Rennes (IRMAR) 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
 Domain : Mathematics/StatisticsStatistics/Statistics Theory
 Keywords: 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