中文摘要：

在非参数统计中,局部多项式回归是重要的工具,然而以往研究的算法基本都是非递推的.本文研究递推的局部线性回归估计及其应用.首先推导出递推算法,给出了回归函数及其导函数的非参数估计.在一定的条件下,证明了算法的强一致性.并且通过仿真例子研究了它在非线性条件异方差模型的回归函数估计和非线性ARX（nonlinearautoregressive system with exogenous inputs,NARX）系统辨识中的应用.

英文摘要：

In nonparametric statistics, local polynomial regression is one of the most important tools. However, almost the previous work is based on nonrecursive algorithms. We investigate the recursive local linear regression estimation. The recursive algorithms are derived for the nonparametric estimation of the regression function and its derivative. Strong consistence of the estimates is established under reasonable conditions. The applications to estimation of the regression model with nonlinear conditional heteroskedasticity and identification of the nonlinear ARX （NARX） system are demonstrated by numerical simulation.