| Type of document: |
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Research report |
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| Domain: |
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| Title: |
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On the Rate of Convergence of the Bagged Nearest Neighbor Estimate |
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| Author(s): |
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Gérard Biau ( ) 1, Frédéric Cérou () 2, Arnaud Guyader ( Author to contact preferably |
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| Research team(s): |
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| Abstract: |
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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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| Other classification: |
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AMS 2000 Classification : 62G05, 62G20 |
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| Full text language: |
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English |
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| Report type: |
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Research Report |
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| Page number: |
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28 |
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| Publication date: |
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2009 |
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| Keywords: |
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Bagging – Resampling – Nearest neighbors – Rates of convergence. |
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| Internal note: |
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RR-6860 |
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