Inference for nonsmooth regression curves and surfaces using kernel-based methods

In this paper we review kernel-based methods for detecting discontinuities in an otherwise smooth regression function or surface. In case of a possible discontinuous curve the interest might be in detecting the discontinuities, their jump sizes and finally to estimate the discontinuous curve. Alternatively, one might be uniquely interested in estimating directly the discontinuous curve preserving the jumps. A brief discussion on available kernel-based methods for testing for a continuous versus a discontinuous regression function, and for detecting discontinuities in regression surfaces is also provided.