Loch Linear Fitting under Near Epoch Dependence: Uniform Consistency with Convergence Rate

Local linear fitting is a popular nonparametric method in nonlinear statistical andeconometric modelling. Lu and Linton (2007) established the point wise asymptoticdistribution (central limit theorem) for the local linear estimator of nonparametricregression function under the condition of near epoch dependence. We furtherinvestigate the uniform consistency of this estimator. The uniformly strong andweak consistencies with convergence rates for the local linear fitting areestablished under mild conditions. Furthermore, general results of uniformconvergence rates for nonparametric kernel-based estimators are provided.Applications of our results to conditional variance function estimation and someeconomic time series models are also discussed. The results of this paper will beof widely potential interest in time series semiparametric modelling.