Nonparametric Change Point Estimation And Application Based On Binary Segmentation

The problem of change point is one of the hot issues in statistics in recent years,it is not only an important branch of statistical inference,but also has high application value in traffic research,disaster prediction and medical diagnosis.Binary segmentation method is a common technology in change point research,but the binary segmentation change point detection algorithm cannot accurately detect the situation that the distance between two adjacent change points is too small,in view of this limitation,based on previous studies,this paper discusses the non-parametric change point detection problem of BS change point detection algorithm with Cusum-Ks(Cumulative Sum-Kolmogorov Smirnov)as the test statistic,and aims to study more efficient nonparametric change point detection algorithms which based on the binary segmentation change point detection algorithm.The specific work are as follows.First,based on the nonparametric model of the cumulative distribution function,using sample observations to estimate the cumulative distribution function of the population,combining the Cumulative Sum(CUSUM)and the Kolmogorov Smirnov(KS)statistics to construct the CUSUM-KS test statistic,then prove its convergence.Secondly,in view of the defect that the binary segmentation method cannot accurately identify two adjacent change points,according to theoretical research,select the set statistic threshold,given the minimum distance between the change points and the hypothesis of the jump degree,and obtain the nonparametric binary segmentation change point detection algorithm(NBS);again,in order to expand the scope of application of the algorithm,adding random interval technology,based on the NBS change point detection algorithm,a more flexible and widely used nonparametric wild binary segmentation change point detection algorithm(NWBS)is obtained.Provide proofs of the consistency of the NBS and NWBS change point detection algorithms respectively.Finally,through a large number of simulation experiments,the NBS and NWBS change point detection algorithms are compared with other algorithms: WBS(Wild Binary Segmentation)?PELT(Pruned Exact Linear Time)?NMCD(Nonparametric Maximum Likelihood Change Point Detection)? BP(Bai J and Perron P)and so on.The results of the simulation experiments show that the NBS and NWBS change point detection algorithms are more efficient and consistent.Especially the NWBS change point detection algorithm,it continues to maintain the consistency and accuracy of the change point estimation when the NBS change point detection algorithm is not applicable.Its absolute error of the change point estimation and two edges of the Hausdorff distances are smaller than other algorithms,indicating its estimation performance Better.In order to verify the effect of the NBS and NWBS change point detection algorithms on actual data,we uses traffic data and stock data as the research objects to conduct empirical analysis respectively.The results show that both algorithms can better identify the change points in the data,obtain its inherent laws,and the detected change points are highly explanatory and in line with the actual situation,which can provide reference opinions for relevant departments to make decisions,so has certain practical application value.