# Inference for Change Points in High Dimensional Mean Shift Models

arXiv: https://arxiv.org/abs/2107.09150 · HTML: https://mlsanity.com/paper/2107.09150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 19 Jul 2021.

## Builds on (most cited first, 10 of 10)

- [Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression](https://mlsanity.com/paper/1804.02605/) (2018)
- [High-dimensional changepoint estimation via sparse projection](https://mlsanity.com/paper/1606.06246/) (2016)
- [Multiple Change-point Detection: a Selective Overview](https://mlsanity.com/paper/1512.04093/) (2015)
- [Multiscale Change-Point Inference](https://mlsanity.com/paper/1301.7212/) (2013)
- [Minimax rates in sparse, high-dimensional changepoint detection](https://mlsanity.com/paper/1907.10012/) (2019)
- [Localizing Changes in High-Dimensional Regression Models](https://mlsanity.com/paper/2010.10410/) (2020)
- [Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise](https://mlsanity.com/paper/2005.01379/) (2020)
- [Change Point Estimation in Panel Data with Temporal and Cross-sectional Dependence](https://mlsanity.com/paper/1904.11101/) (2019)
- [Inference on the Change Point for High Dimensional Dynamic Graphical Models](https://mlsanity.com/paper/2005.09711/) (2020)
- [Segmentation of high dimensional means over multi-dimensional change points and connections to regression trees](https://mlsanity.com/paper/2105.10017/) (2021)

## Abstract (arXiv)

We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. 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 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 change point parameters. The 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.