  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, compared to an existing method in literature.
