Inference for Change Points in High Dimensional Mean Shift Models

Detection of change points constitutes a canonical statistical problem due to numerous applications in diverse areas, including economics and finance (Basseville et al. [1993], Frisén [2008]), quality process control (Qiu [2013]), functional genomics and neuroscience (Koepcke et al. [2016]). The offline version of the problem, wherein one examines the data retrospectively and aims to detect the presence and/or location of change points has been studied extensively for a variety of statistical models, including signal plus noise, regression, graphical, random graph, factor and time series models and various algorithms have been developed to accomplish this task -dynamic programming, regularized cost functions, binary segmentation, multiscale methods, etc., see, e.g. the review article Niu et al. [2016]. In the presence of multiple change points, consistency of the estimated location of the change points under certain regularity assumptions on the temporal spacing between change points and on the magnitude of the changes in the underlying model parameters have been established, see, e.g. Fryzlewicz [2014], Frick et al. [2014] and Wang and Samworth [2018] amongst several others, here the former two are under a fixed p framework and the latter under a high dimensional framework. Further, when a single change point has been assumed, the asymptotic distribution of the change point estimator has been established for various statistical models, see, e.g., [Bai, 1994, 1997], Csorgo and Horváth [1997], under fixed p setting, and [Bhattacharjee et al., 2017, 2019], [Kaul et al., 2020, 2021], under diverging dimensionality, where the last two articles allow potential high dimensionality.