Year: 2023
Type: article
Abstract: We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model.We develop a locally refitted least squares estimator and obtain component-wise and simultaneous rates of estimation of change points.The simultaneous rate is the sharpest available by at least a factor of log p, while the component-wise one is optimal.These results enable existence of limiting distributions for the locations of the change points.Subsequently, component-wise distributions are characterized under both vanishing and non-vanishing jump size regimes, while joint distributions of change point estimates are characterized under the latter regime, which also yields asymptotic independence of these estimates.We provide the relationship between these distributions, which allows construction of regime adaptive confidence intervals.All results are established under a high dimensional scaling, in the presence of diverging number of change points.They are illustrated on synthetic data and on sensor measurements from smartphones for activity recognition.
Source: Statistica Sinica
Authors: Abhishek Kaul, George Michailidis
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W3186461132