## Section: New Results

### Rate of convergence of the bagged nearest neighbor estimate

Participants : Frédéric Cérou, Arnaud Guyader.

See 3.5

This is a collaboration with Gérard Biau, from université Pierre et Marie Curie, ENS Paris and INRIA Paris Rocquencourt (project–team CLASSIC).

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 subsample, and decide by combining. By bagging an
n -sample, the crude nearest neighbor regression estimate is turned
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} and k_{n}/n0 ,
we have shown that this estimate achieves optimal rate of convergence,
independently from the fact that resampling is done with or without
replacement. Since the estimate with the optimal rate of convergence
depends on the unknown distribution of the observations, adaptation
results by data–splitting are also obtained [12] , [24] .