Nonparametric regression analysis is an important and popular method to investigate the regression model of the source of data. Traditionally, regression analysis is often used under the assumption that the regression function is continuous and smooth. However in a real world situation, it is quite common that due to the presence of an external force, the regression function has change points. Because of the boundary effect of change points, the estimated regression function derived by nonparametric regression method may be far from the real model. Since the kernel estimator of a nonparametric regression function is simple and has nice asymptotic properties, it has been widely used in estimating the regression function. However, apart from being dependent on the choice of a smoothing parameter, these nice properties depend on the continuity of the regression function. From recent researches, we have learned that the ignorance of the possible existence of change points will lose the nice properties of the kernel estimator of a regression function. Therefore, it is very important to decide whether a change point is present somewhere. In this article, we shall use the L-2 norms of the DKE (difference between two kernel estimators) which are proposed in Wu and Chu (1993) to construct a new estimator to test whether the change point exists or not. We shall also derive the limiting distribution of this test estimator.
Tamsui Oxford Journal of Mathematical Sciences 14, pp.1-10