The Change-point Detection Problem Of Mean Model In Panel Data

In this thesis,we discuss mainly the estimation and the statistical inference of change-point problems in means for panel data.The full thesis is divided into four chapters:In Chapter 1,we review the history study of change-point detections.And then the preliminary knowledge about the CUSUM estimation and panel data is introduced.Lastly,we describe our main results.In Chapter 2,we see that as the one of the scholars who did research early in change-point detection for a mean shift model for panel data,J.S.Bai proposed a least squares estimator(LSE)for the common change-point in reference[16]in 2010,then the consistency of the LSE in proved and the convergence rate is calculated.In this chapter,for the same change-point model in panel data,we propose a new CUSUM estimator for the common change-point.We also establish the consistency of the estimated change-point,and provide the corresponding convergence rate.Monte-Carlo simulation shows that the CUSUM method is more efficient than that of reference[16]in two perspectives which include precision and computational complexity of the estimator.In Chapter 3,we study the statistical inference of change-point for panel data.Firstly,we establish a sequential panel data model and the hypothetical test for change-point,then the test statistic is constructed and the limiting distribution is obtained.Secondly,according to the theory results,we propose an asymptotic method and a new bootstrap method.Many scholars developed bootstrap method for the test of change-point in univariate series in recent years.So far,the using of bootstraps in all the thesis are discussed only for the univariate series.Based on this facts,we develop the new bootstrap method to the sequential change-point tests for panel data,which is more complex.lastly,we have the validity of the bootstrap tests in theory and compare two tests in simulations.Moreover,we introduce the sequential ideas in bootstrap method,then the critical value is adjusted with the coming of the new observations and we realize the on-line monitoring really.In Chapter 4,we summarize the main results of this thesis and propose some interesting problems to be done.