Consistency for cross-validated nearest neighbor estimates in nonparametric regression (Q793461)

It is shown that the cross-validated nearest neighbor estimate of a regression function f is consistent, where \(y_ i=f(x_ i)+\epsilon_ i\), \(i=1,2,...\), are the observed data (assumed to be bounded), \(\{x_ i\}\) is a well-spaced non-random design in \({\mathbb{R}}^ p\) and \(\{\epsilon_ i\}\) are independent zero mean errors.