Single-Step Change Point Estimation In Nonlinear Profiles Using Maximum Likelihood Estimation

In this work, we study the change point problem in nonlinear profiles. A maximum likelihood estimator (MLE) is proposed for single step change point detection in nonlinear profiles. Due to the complexity of estimating the parameters of the nonlinear model by MLE, this estimator is based on the difference between the response variables and in-control profile curve with no need of estimating the regression parameters. Since the likelihood function (or its logarithm) is complicated enough to deter one from estimating the time of change by an exact method we resort to techniques in numerical analysis for this purpose. Finally, the performance of the proposed estimator is tested through simulation studies.