Inference for Change Points in High-Dimensional Mean Shift Models

• Activity Number: 205 - Inference on Functional Data
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Abhishek Kaul* and George Michailidis
• Companies: Washington State University and U Florida
• Keywords: Multiple change points; High dimensional; Optimal estimation; Inference; Limiting distributions; Regime adaptation

Abstract

We consider the problem of constructing confidence intervals for change points in a high-dimensional mean shift model. We develop a locally refitted least squares estimator and obtain componentwise and simultaneous rates of estimation of change points. Simultaneous rate is the sharpest available in the literature by at least a factor of log p, while the component-wise is optimal. This enables existence of limiting distributions. Distributions are characterized under both vanishing and non-vanishing jump size regimes. Results are used to construct asymptotically valid component-wise and simultaneous confidence intervals for the change point parameters. We provide the relationship between these distributions, which allows construction of regime (vanishing vs non-vanishing) adaptive confidence intervals. All results are established under a high dimensional scaling, allowing for diminishing jump sizes, in the presence of diverging number of change points and under subexponential errors. They are illustrated on synthetic data and on sensor measurements from smartphones for activity recognition.