Empirical likelihood test in a posteriori change-point nonlinear model

Abstract

In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The asymptotic distribution of the test statistic under the null hypothesis is obtained, which allows to find the asymptotic critical value. On the other hand, we prove that the proposed test statistic has the asymptotic power equal to 1. These theoretical results allows find a simple test statistic, very useful for applications. The epidemic model, a particular model with two change-points under the alternative hypothesis, is also studied. Numerical studies by Monte Carlo simulations show the performance of the proposed test statistic.