Statistical Inference In The Location Parameter Change-point Estimator

Change-point problem has been a hot topic in statistics since the 1970s. It is widely used in industrial quality control (one of the earliest areas that generate Change Point Problems statistical research), economic, medical, financial and other fields.In this paper, we constructthe anti-symmetric kernel function and proposed the change point estimator with the help of CUSUM method and U-statistics method to discussthe statistical properties of the location parameter change point estimator, and are divided in four chapters to introduce.In chapterl,we first give a brief overview of the origin and the development of change point problems. Then wefocus on the research status of the location parameter change point model and the application of U-statistic methods in statistical inference problems. Furthermore, we describe the research status of asymptotic distribution in change point statistical inference.Finally,a brief description of the main contents and findings of this paper is given.The second chapter investigates the model which has only one location parameter change point, we use the cumulative sum (CUSUM) method to give a statistical estimator of the change point,and then investigate the consistency and convergence rate of the estimator under the assumption that the degree of changeis constant. Furthermore,weinvestigate the consistency and convergence rate of the estimator under the assumption that the degree of change is not constant (θ=θnâ†' 0, nâ†'∞).In chapter 3,we do the simulation analysis about location parameter change point model and the simulation results show that our methods are effective.The last chapter gives the summary about this paper,andthe future research tendency of change point is also discussed in chapter 4.