ON ESTIMATING REGRESSION FUNCTION WITH CHANGE POINTS

Local polynomial fitting has been known as a powerful
nonparametric regression method when dealing with correlated data and when trying to find implicit connections between variables. This method relaxes
assumptions on the form of the regression function under investigation. Nevertheless, when we try fitting a regression curve with precipitous changes using general local polynomial method, the fitted curve is oversmoothed near points where the true regression function has sharp features. Since local polynomial modelling is fitting a "polynomial", a continuous and smooth function, to the regression function at each point of estimation, such drawback is intrinsic. Here, we suggest a modified estimator of the conventional local polynomial method. Asymptotic mean squared error is derived. Several numerical results are also presented.