Ornstein-Uhlenbeck 型过程多变点检验及两样本检验问题

This project mainly studies multiple-change-point detection problem for structure parameters and two-sample test problems for the process of Ornstein-Uhlenbeck type. The main focuses are as follows. I) Based on the sparsified binary segmentation algorithm, we study the multiple-change-point detection problem for the process of Ornstein-Uhlenbeck type, and discuss the asymptotic size and power. II) Based on the empirical characteristic function and Bootstrap method, we study the two-sample test problem for the process of Ornstein-Uhlenbech type, using two-step testing method. In this project, we will investigate the finite sample performance of the proposed test statistics by simulation studies, and apply the new tests to real data analysis.

本课题针对Ornstein-Uhlenbeck型过程研究结构参数的多变点检验问题和两样本检验问题。主要的研究内容：一、基于稀疏的二元分割算法，研究Ornstein-Uhlenbeck型过程的多变点检验问题，并讨论该检验的渐近第一类错误和功效。二、利用经验特征函数，结合Bootstrap方法，采用两步检验的方法，研究Ornstein-Uhlenbeck型过程的两样本检验问题，并讨论该检验的渐近第一类错误和功效。同时，在本课题的研究中，将通过大量的计算机模拟实验，考察所提检验统计量的有限样本性质，并将这些检验方法应用于实际数据的分析。