Cross‐validation and non‐parametric k nearest‐neighbour estimation

Abstract

Summary In this paper we consider the problem of estimating a non-parametric regression function using the k nearest-neighbour method. We provide asymptotic theories for the least-squares cross validation (CV) selected smoothing parameter k for both local constant and local linear estimation methods. We also establish the asymptotic normality results for the resulting non-parametric regression function estimators. Some limited Monte Carlo experiments show that the CV method performs well in finite sample applications.