On the mutual nearest neighbors estimate in regression

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