Study On Multiple Change-point Problems And Its Application Based On Nonparametric Methods

Change-point problem has been a hot topic in statistics since the 1970, which has originally arisen in the context of quality control. It is also widely used in many natural and social fields such as economic, finance, climate and traffic science. In this thesis, we discuss mainly multiple change-point problems of independent random sequences with nonparametric methods and its application in traffic.Two important issues in multiple change-point problems are the number and location estimations of change-point, which would be studied with two kinds of nonparametric methods in this paper.Considering the inner link of change-point problem and two samples problem, we transform the existence test of change-point into goodness-of-fit test of two distributions by Kolmogorov-Smirnov(K-S) test. Then we discuss change-point existence hypothesis test and location estimation by sliding window method. Combing with the method of bisection, the number and location of multiple change-point are estimated. Lastly, change-point simulations of different distribution types by Matlab are displayed, it is shown that our procedures are rather effective. And as a practical application of multiple change-point, we research the traffic volume data of central roads of Guiyang City by the above method.Another is nonparametric method based on maximum likelihood to discuss multiple change-point, which is discussed under two situations of known and unknown change-point number. As is known, there is a corresponding cumulative distribution function of any random variables, and it can reflect all the information of samples. So when the change-point number is known, we provide location estimator by maximum likelihood function of empirical cumulative distribution function and present the consistency of location estimator. In the case of unknown change-point number, we use Bayesian information criterion(BIC) to strike a balance between the likelihood and the number of change-point by incorporating a penalty for change-point number. The change-point number and location estimators are provided by minimizing the BIC, and the convergence of change-point number is also considered. Finally, we use dynamic programming(DP) algorithm to solve the likelihood function under the first situation, and simulations of different distribution types by R are also displayed, the results show the effectiveness of the method. And then the traffic volumn data of Public Security intersection of Guiyang City is studied for the second situation, and the reaults show that the method is more desirable than parametric methods for the traffic data change-point analysis.