Nonparametric CUSUM change-point detection procedures based on modified empirical likelihood

Sequential change-point analysis, which identifies a change of probability distribution in a sequence of random observations, has important applications in many fields. A good method should detect the change point as soon as possible, and keep a low rate of false alarms. As an outstanding procedure, Page’s CUSUM rule holds many optimalities. However, its implementation requires the pre-change and post-change distributions to be known which is not achievable in practice. In this article, we propose a nonparametric-CUSUM procedure by embedding different versions of empirical likelihood by assuming that two training samples, before and after change, are available for parametric estimations. Simulations are conducted to compare the performance of the proposed methods to the existing methods. The results show that when the underlying distribution is unknown and training sample sizes are small, our modified procedures exhibit advantages by giving a smaller delay of detection. A well-log data is provided to illustrate the detection procedure.