Kernel estimation of discontinuous regression functions

Abstract

A kernel regression estimator is proposed wherein the regression function is smooth, except possibly for a finite number of points of discontinuity. The proposed estimator uses preliminary estimators for the location and size of discontinuities or change-points in an otherwise smooth regression model and then uses an ordinary kernel regression estimator based on suitably adjusted data. Global L2 rates of convergence of curve estimates are derived. It is shown that these rates of convergence are the same as those for ordinary kernel regression estimators of smooth curves. Moreover, pointwise asymptotic normality is also obtained. The finite-sample performance of the proposed method is illustrated by simulated examples.