A universal strong law of large numbers for conditional expectations via nearest neighbors

For k(n)-nearest neighbor estimates of a regression Y on X (d-dimensional random vector X, integrable real random variable V) based on observed independent copies of (X, Y), strong universal pointwise consistency is shown, i.e., strong consistency P-X-almost everywhere for general distribution of (X, Y). With tie-breaking by indices, this means validity of a universal strong law of large numbers for conditional expectations E(Y\X = x). (C) 2007 Elsevier Inc. All rights reserved.