Cross Validation and Non Parametric K Nearest Neighbour Estimation
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. Copyright Royal Economic Society 2006