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Cross-validation and non-parametric \(k\) nearest-neighbour estimation. (English) Zbl 1106.62043
Summary: We consider the problem of estimating a nonparametric 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 nonparametric regression function estimators. Some limited Monte Carlo experiments show that the CV method performs well in finite sample applications.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65C05 Monte Carlo methods
Software:
SemiPar
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