On sequential nearest neighbour regression estimation

Abstract

For the problem of estimating E(Xn+1 | Xn = x) for a discretetime Markov process, Yakowitz (1993) introduced a nearest neighbour estimator with random sample size where sampling is done until the kth visit to a small ball around x occurs. He proves consistency for such prodcedures of this type for the general regression problem and show consistency for φ-mixing processes under short range dependence.