Nonparametric Estimation Of Jump Surface

In this paper, we discuss estimation of bivariate jump regression functions. An a.s. consistent estimator of the jump location curve is suggested. This estimator is based on difference of two one-sided kernel smoothers. A rotation transformation is also used. We consider an ideal case that the jump location curve has an explicit function form first and then generalize it to a more general case that the explicit function form does not exist. Comparing to some existing methods on this topic, mainly to the edge detection methods in image processing literature, our method uses less conditions on the design points and on the underlying regression function. So it is expected to find more applications