U-Statistic Based Modified Information Criterion for Change Point Problems

The U-statistic based modified information criterion (MIC) is proposed and applied to detect the change point in a sequence of independent random variables. In this article, we show that the method is consistent in selecting the correct model, and the resulting test statistic has a simple limiting distribution. We investigate the method based on both symmetric and anti-symmetric kernel functions. The simulation results indicate that the new method has better power in detecting the changes compared to other methods, such as the likelihood based MIC (Chen et al., 2006 Chen , J. , Gupta , A. K. , Pan , J. ( 2006 ). Information criterion and change point problem for regular models . Sankhyā 68 : 252 – 282 . Google Scholar]) and the Bayesian information criterion of Schwarz (BIC, Schwarz, 1978 Schwarz , G. ( 1978 ). Estimating the dimension of a model . Ann. Statist. 6 : 461 – 464 .Crossref], Web of Science ®] , Google Scholar]).