| Nonparametric function estimation via local polynomial regression has been widely studied in the literature, especially in the past two decades. In practice, we confront two challenges. Firstly, the local least squares estimator may not be the best choice when errors are heavily tailed. Secondly, the data are correlated. In this thesis, we propose robust local linear smoothing procedures to cope with nonparametric regression and varying coefficient models with the random error following a possible heavily tailed autoregressive (AR) process. Unlike classical local linear technique, our method takes into account the specific error structure. This correlation information allows us to improve the estimation efficiency. Furthermore, by applying robust regression techniques, the new method is insensitive to outliers comparing with corresponding least squares approaches. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance. From our simulation studies, we find that the newly proposed procedures dramatically improve the accuracy over classical procedures under working-independence. |
