Detecting change structures of nonparametric regressions

Abstract

This research investigates detecting change points of general nonparametric regression functions by introducing a novel criterion. It is based on the moving sums of conditional expectation to avoid both computationally expensive algorithms, exhaustive search methods need, and false positives hypothesis testing-based approaches encounter. This new criterion can simultaneously and consistently, in a certain sense, detect multiple change points and their locations even when, as the sample size goes to infinity, the number of changes grows up to infinity, and some changes tend to zero. Further, because of its visualization nature, in practice, the locations can be relatively more easily identified, by plotting its signal statistic, than existing methods in the literature. Numerical studies are conducted to examine its performance in finite sample scenarios, and a real data example is analyzed for illustration.