| Abstract: | In this paper we use non-parametric local polynomial methods to estimate the regression function, m ( x ). Y may be a binary or continuous response variable, and X is continuous with non-uniform density. The main contributions of this paper are the weak convergence of a bandwidth process for kernels of order (0, k ), k =2 j , j ≥1 and the proposal of a local data-driven bandwidth selection method which is particularly beneficial for the case when X is not distributed uniformly. This selection method minimizes estimates of the asymptotic MSE and estimates the bias portion in an innovative way which relies on the order of the kernel and not estimation of m 2( x ) directly. We show that utilization of this method results in the achievement of the optimal asymptotic MSE by the estimator, i.e. the method is efficient. Simulation studies are provided which illustrate the method for both binary and continuous response cases. |
