Recursive local polynomial regression estimation and its applications

In nonparametric statistics, local polynomial regression is one of the most important tools. However, almost the previous works are based on nonrecursive algorithms. Taking the linear case as an example, the paper considers recursive local polynomial regression estimation, the recursive algorithms are derived for the regression function and its derivative. The strong consistence has also been established under reasonable conditions. Finally its applications to estimation of the regression function of the nonlinear autoregressive conditional heteroskedasticity (NARCH) model and identification of the nonlinear ARX (NARX) system are demonstrated by numerical simulation.