Residual variance estimation using a nearest neighbor statistic

In this paper we consider the problem of estimating E[(Y−E[Y∣X])2]E[(Y−E[Y∣X])2] based on a finite sample of independent, but not necessarily identically distributed, random variables (Xi,Yi)i=1M. We analyze the theoretical properties of a recently developed estimator. It is shown that the estimator has many theoretically interesting properties, while the practical implementation is simple.