LOCAL POLYNOMIAL ESTIMATION OF REGRESSION-FUNCTIONS FOR MIXING PROCESSES

Local polynomial fitting has many exciting statistical properties whic h where established under i.i.d. setting. However, the need for non-li near time series modeling, constructing predictive intervals, understa nding divergence of non-linear time series requires the development of the theory of local polynomial fitting for dependent data. In this pa per, we study the problem of estimating conditional mean functions and their derivatives via a local polynomial fit. The functions include c onditional moments, conditional distribution as well as conditional de nsity functions. Joint asymptotic normality for derivative estimation is established for both strongly mixing and p-mixing processes.