Research On Change-point Detection Based On Revised BJ Method

Change-point detection is one of the hottest issues in the study of statistics, and it has been extended to industrial, economic, financial, genetic and signal process, and other fields.On the other hand, we can only observe data information or part of the population information in most of the time, do not know anything about the distribution type of the population. At this time, how to study change-point detection is a very difficult job. Thesis plans to do some exploration work in this aspect.The paper is based on the research of Zou Changliang etc.(2014), using revised Berk-Jones test function, and using maximum likelihood method to discuss change-point problem. The pur-pose of using revised Berk-Jones test function is mainly because in the large sample case, they have the same limit properties with the empirical likelihood method.And in terms of small sam-ple simulation, in some cases, use it to construct the test has higher efficacy. Specifically, we firstly replace the empirical likelihood function in the paper of Zou Changliang etc.(2014) with revised Berk-Jones test function, and then construct new likelihood function; diagnose the number and locations of the change-point, and estimate the distribution of every data segment at the same time; discuss their statistical properties, mainly is limit properties under the occasion of a large sample; Finally give some simulation comparisons. In theory, we get the asymptotic properties of the method, the consistency of the algorithm and faster convergence speed, etc. Simulation result shows that, under some certain circumstances, our method can rapidly and accurately detect the number and the locations of change-point.In this paper, the main contribution of the paper are summarized as follows:1. The use of the maximum likelihood method reduces the assumptions about the distribution and the model, so as to avoid the wrong model assumes. Using revised BJ test statistics, makes theoretical proof and algorithm more concise and clear.2. Under some relatively loose conditions, we can prove that without any distribution as-sumptions for the estimate of the change-point, non-parametric change-point detection method can achieve faster convergence speed.3. The simulations show that the proposed test statistics based on the revised BJ can more quickly and efficiently estimate the number and the locations of the changing-points.In the actual life and work, many data sequences are unknown, also cannot verify their clear distributions, our conclusion and method provides a feasible approach for the change-point detec-tion.