Section: New Results

Mutual nearest neighbors

Participant : Arnaud Guyader.

This is a collaboration with Nicolas Hengartner (Los Alamos).

Motivated by promising experimental results, this work [13] investigates the theoretical properties of a recently proposed nonparametric estimator, called the MNR (mutual nearest neighbors) rule, which estimates the regression function $m\left(x\right)=E\left[Y\right|X=x]$ as follows: first identify the $k$ nearest neighbors of $x$ in the sample, then keep only those for which $x$ is itself one of the $k$ nearest neighbors, and finally take the average over the corresponding response variables. We prove that this estimator is consistent and that its rate of convergence is optimal. Since the estimate with the optimal rate of convergence depends on the unknown distribution of the observations, we also have adaptation results by data-splitting.