Detecting change point in linear regression using jackknife empirical likelihood

Abstract

Data generated in quite a few examples can be described using a linear regression model with a change point. In this paper for such a model, we develop a nonparametric method based on the jackknife empirical likelihood (JEL) to detect the change in regression coefficients. Under mild conditions, we show that the null distribution of the JEL ratio test statistic is asymptotically Gumbel. The test and the estimator of change point are shown to be consistent under the alternative hypothesis. Simulation suggests that the proposed method is computationally much more affordable than the alternative based on empirical likelihood. We also demonstrate the proposed method using two real datasets.