Empirical Likelihood-Based CUSUM Method

• Activity Number: 576
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Yijie Xue*+ and Nicole A. Lazar
• Companies: University of Georgia and University of Georgia
• Keywords: Sequential probability ratio test

Abstract

The changepoint detection problem is an important topic in fields such as climate science, quality control and finance. We propose an empirical likelihood based cumulative sum approach based on the idea of Page's cumulative sum method for simple null and alternative hypotheses which means the parameter is equal to one value in either hypothesis. Under mild conditions, we prove the optimality of the proposed stopping time in the sense of Lorden (1971) without model assumptions. We also discuss the situation of composite null hypothesis and simple alternative hypothesis, meaning the true value is from a range of values in the null hypothesis, and prove upper bounds for the expectation of the proposed stopping time with respect to the values in the null and alternative hypotheses respectively. Simulations and a real example application are given, followed by the conclusion and discussion.