Residual variance estimation using a nearest neighbor statistic

In this paper we consider the problem of estimating E [ ( Y − E [ Y ∣ X ] ) 2 ] based on a finite sample of independent, but not necessarily identically distributed, random variables ( X i , Y i ) i = 1 M . 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.