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 as follows: first identify the nearest
neighbors of in the sample, then keep only those for which is itself
one of the 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.