Cross-validated local linear nonparametric regression
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Local linear kernel methods have been shown to dominate local constant methods for the nonparametric estimation of regression functions. In this paper we study the theoretical properties of cross-validated smoothing parameter selection for the local linear kernel estimator. We derive the rate of convergence of the cross-validated smoothing parameters to their optimal benchmark values, and we establish the asymptotic normality of the resulting nonparametric estimator. We then generalize our result to the mixed categorical and continuous regressor case which is frequently encountered in applied settings. Monte Carlo simulation results are reported to examine the finite sample performance of the local-linear based cross-validation smoothing parameter selector. We relate the theoretical and simulation results to a corrected AIC method (termed AIC c) proposed by Hurvich, Simonoff and Tsai (1998) and find that AIC c has impressive finite-sample properties.
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