Energy statistic-based modified information criterion for detecting the change in distribution

In this article, a test to detect the change in the distribution of sequence of independent random variables is proposed. To achieve this, we exploit the relationship between properties of U-statistics and Energy statistics (forms of V-statistics) to come up with a nonparametric test based on modified information criterion (MIC) in the change point detection using Energy statistics (EMIC). To investigate the performance of our proposed (EMIC) method, we assess the finite sample properties and compare efficiencies and powers of different methods with those of our method through simulations. Both the test procedure and the estimator of the location of the change point are consistent under the alternative hypothesis. In addition, simulation studies suggest that the proposed (EMIC) method is superior to other methods especially when the change occurs around the middle of the sequence. We then discuss its applications in two different real-life examples for detecting change in mean and variance.