Some Aspects of Change Point Analysis

In the first part of the dissertation, we propose two tests with the purpose of detecting change point in a sequence of independent random variables. Both the consistency and rate of convergence of the estimated change point are established. We then extend the application of the proposed test in the field of multiple change points detection problem. Simulation studies and real data analysis are given to examine the performance of our proposed methods.

In the second part of the dissertation, we propose a procedure for detecting multiple change points in a mean-shift model, where the number of change points is allowed to increase with the sample size. A theoretic justification for our new method is also given. The proposed procedure is implemented in an algorithm which, compared to two popular methods via simulation studies, demonstrates satisfactory performance in terms of accuracy, stability and computational complexity. Finally, we apply our new algorithm to analyze two real data examples.

In the third part of the dissertation, our research is motivated by HIV viral dynamic studies. We jointly model HIV viral dynamics, CD4 process with measurement errors and change point model, and estimate the model parameters simultaneously via the Monte Carlo EM approach and hierarchical likelihood approximation approach. These approaches are illustrated in a real data example. Simulation results show that both of these two methods perform well and are much better than the commonly used naive method.