On detection of change points using mean vectors

In this paper, the authors consider the problem of change points within the framework of model selection and propose a procedure for estimating the locations of change points when the number of change points is known. The strong consistency of this procedure is also established. The problem of detecting change points is discussed within the framework of the simultaneous test procedure. The case where the number of change points is unknown will be discussed in another paper.This project is supported by the National Natural Science Foundation of China and by the Air Office of Scientific Research of the United States.