Nonparametric estimation of the regression function having a change point in generalized linear models

In this paper, the local polynomial fit based on the kernel weighted local-likelihood function and the location of the change point is considered as an estimator for the regression function or its νth derivative. Using the data sets split by the location, we estimate the left and right parts of the regression function or its νth derivative. The global L2 rate of convergence of the estimated function is derived. The finite-sample performances of the proposed estimators are illustrated using simulated and real examples.