An Improved Local-linear Estimator For Nonparametric Regression With Autoregressive Errors

In this paper we propose a modification of the local linear smoother to account for the autocorrelated errors in a nonparametric regression model with random-design. The proposed estimator has a closed-form expression and is simple to calculate. The asymptotic bias and variance of the proposed estimator are studied for AR(1) case. Compared to the standard local linear smoother, the proposed estimator retains the same design-adaptive bias but has a smaller asymptotic variance. Therefore the proposed method improves the estimation efficiency in kernel regression