The Application And The Statistical Inference About Change Point Problems

In the mathematical statistics, the research of change points is a new problem comparatively. Commonly, it was thought that the research of change points started in 1954, when Page published a thesis about continuous sampling inspection in Biometrika. The change point problems appeared early in industry automation. Subsequently, many statisticians devoted into this research field, and some theoretic and applied papers about the change points were published. Now, a great deal mature results about the change point problems have been published, for example, Csorgo and Horváth "Limit theorem in change-points analysis "in 1997,that is a theory research sum up recently. Some research methods of the change point problem are continually developed, for example, the maximum likelihood method, (weighted) least square method, the non-parametric method and Bayasian method etc. change point problems occur not only in industry automation early, but also in many natural and social fields such as economics, finance, medicine and meteorology etc. In this paper, we first use the linear regression model to analyze the relation of the residents'deposit and income, and introduce change point analysis to study the problem of the relation has structural change in an unknown time point.; then we use a Bayesian analysis and an information approach to detect a change-point in a sequence of independent random variables from exponential family distributions. The Bayesian Schwarz information criterion is derived. After that, we discuss the hypothesis tests and estimation for most one change point in the linear structural error-in-variables model. In the last, we use the method given by Lajors Horvath estimate the change point of Yen-Dollar exchange rates series.