Empirical likelihood test in a posteriori change-point nonlinear model

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. The asymptotic behaviour of the empirical likelihood statistic under the null hypothesis and its alternative is studied. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The critical value is chosen so that the test has a small probability of a false alarm and asymptotic power one. 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, compared to an existing method in literature, for models without change or with one or two change-points.