CROSS-VALIDATED LOCAL LINEAR NONPARAMETRIC REGRESSION

Abstract

Abstract: 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 selec-tion 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 AICc) proposed by Hur-vich, Simonoff and Tsai (1998) and find that AICc has impressive finite-sample properties. Key words and phrases: Asymptotic normality, data-driven bandwidth selection, discrete and continuous data, local polynomial regression. 1.