Change point localisation and inference

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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.