CMStatistics 2021: Start Registration
View Submission - CMStatistics
B1589
Title: Inference for change points in high dimensional mean shift models Authors:  Abhishek Kaul - Washington State University (United States) [presenting]
George Michailidis - U of Florida (United States)
Abstract: The problem of constructing confidence intervals for the locations of changepoints in a high-dimensional mean-shift model is considered. To that end, we develop a locally refitted least squares estimator and obtain component-wise and simultaneous rates of estimation of the underlying change points. The simultaneous rate is the sharpest available in the literature by at least a factor of log p, while the component-wise one is optimal. These results enable the existence of limiting distributions. Component-wise distributions are characterized under both vanishing and non-vanishing jump size regimes, while joint distributions for any finite subset of change point estimates are characterized under the latter regime, which also yields asymptotic independence of these estimates. The combined results are used to construct asymptotically valid component-wise and simultaneous confidence intervals for the changepoint parameters. The results are established under a high dimensional scaling, allowing for diminishing jump sizes, in the presence of a diverging number of change points and under subexponential errors. They are illustrated on synthetic data and on sensor measurements from smartphones for activity recognition.