变点检测，特别是多变点检测问题，一直是统计学研究的主要课题之一，在经济、金融、网络入侵、地质等许多领域都有大量的应用。项目拟基于变量选择中的惩罚思想，主要研究均值模型、线性模型、自回归模型、混合模型（自身历史数据和协变量共同影响的模型）的多变点检测方法。研究的主要思路如下：首先把变点检测问题转化为稀疏变量选择问题；然后利用稀疏变量选择的较新方法，重点是基于惩罚思想的新方法，进行估计或检测，进而讨论相应的统计性质，例如估计的相合性、极限分布等；接着通过模拟给出它们与已有方法的比较；最后把此方法应用到岩溶塌陷数据中。研究过程主要利用惩罚Lq(q>0)，惩罚非参数似然等标准检测方法。之所以选择惩罚Lq(q>0)标准，主要是它包含常见的二乘(q=2)和一乘(q=1)准则，通过对其研究可以得到更为一般的选择标准和选择原则。希望通过此研究寻找到相对一般且切实可行的变点检测方法，并建立相应的理论。

Multiple Change-point detection, has been one of the important research fields in statistics. It can be widely applied into most kinds of subjects, such as economic、finance、network intrusion、geology and so on. Multiple change-point detection methods in mean model、linear model、autoregression model and mixed model are going to be mainly discussed in this project based on penalized ideas. The mixed model includes the influence of historical data(autoregression model) and the influence of covariate data (regression model). The main idea is as follows. First, change-point detection problem will be reconsidered as a sparse variable selection problem. Then change-point estimation、test and their statistical properties, such as consistence、limit distribution and so on, are investigated by using the newer penalized sparse variable selection methods. Next simulation studies are done to compare the new methods with existing methods. At last, the new methods will be applied into the karst collapse data. The penalized Lq(q>0) criterion、penalized nonparametric likelihood criterion are used in the study. Lq(q>0) criterion are considered for its wide expansion. For example, Lq criterion can include least square criterion(q=2)、least absolute deviation criterion(q=1). One general law can be formulated by studying Lq criterion. We hope these discussions can give more powerful and convenient techniques and theories in practice.