Change point localisation and inference

大多数统计工具都是在假设数据是独立的、同分布的情况下进行研究的。这在现实世界中很少发生。当从时间序列、网格图或一般图收集数据时，放松这种假设的一种方法是假设存在恒定区域，其中收集的数据可以假设来自相同的分布。在更均匀的分布假设下，可以在这些恒定区域内进行进一步的统计分析。变点分析就是为这样的过程量身定做的。统计任务包括估计恒定区域，对是否存在异质性进行假设检验，以及导出估计量的极限分布以进一步构造置信度区间或区域。在过去的几年里，各方面的变点分析主要集中在估计方面。推理方面还有待于在许多情况下进行探索。几个可能的项目包括：1、局部平稳时间序列的变点分析。2、整值时间序列的变点分析。动态定价中的变点推理。4.一般图的最优划分推理。

Most of the statistical tools are studied under the assumption that the data are independent and identically distributed. This is rarely the case in the real world. When data are collected from a time series, a grid graph, or a general graph, one way to relax such an assumption is to assume that there are constancy regions where the data collected within can be assumed to be from the same distribution. Further statistical analysis can be conducted within these constancy regions, under more homogenous distributional assumptions. Change point analysis is tailored for such procedures. The statistical tasks include estimating the constancy regions, conducting hypothesis testing on whether there exists heterogeneity, and deriving limiting distributions for the estimators to further construct confidence intervals or regions. In the past few years, various aspects of change point analysis mainly focused on the estimation aspects. The inference aspect is yet to be explored in many settings. A few possible projects include: 1, change point analysis in locally stationary time series. 2, change point analysis in integer-valued time series. 3, change point inference in dynamic pricing. 4, optimal partition inference in general graphs.