In the fixed-design nonparametric regression model, kernel-type estimators of the locations of jump points and the corresponding sizes of jump values of the regression function are proposed. These kernel-type estimators are analyzed with almost sure results and limiting distributions. Using the limiting distributions, we are able to test the number of jump points and give asymptotic confidence intervals for the sizes of jump values of the regression function. Simulation studies demonstrate that the asymptotic results hold for reasonable sample sizes.
"Kernel-Type Estimators of Jump Points and Values of a Regression Function." Ann. Statist. 21 (3) 1545 - 1566, September, 1993. https://doi.org/10.1214/aos/1176349271