# Dating the Break in High-dimensional Data

arXiv: https://arxiv.org/abs/2002.04115 · HTML: https://mlsanity.com/paper/2002.04115/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Segmentation of high dimensional means over multi-dimensional change points and connections to regression trees](https://mlsanity.com/paper/2105.10017/) (2021)

## Abstract (arXiv)

This paper is concerned with estimation and inference for the location of a change point in the mean of independent high-dimensional data. Our change point location estimator maximizes a new U-statistic based objective function, and its convergence rate and asymptotic distribution after suitable centering and normalization are obtained under mild assumptions. Our estimator turns out to have better efficiency as compared to the least squares based counterpart in the literature. Based on the asymptotic theory, we construct a confidence interval by plugging in consistent estimates of several quantities in the normalization. We also provide a bootstrap-based confidence interval and state its asymptotic validity under suitable conditions. Through simulation studies, we demonstrate favorable finite sample performance of the new change point location estimator as compared to its least squares based counterpart, and our bootstrap-based confidence intervals, as compared to several existing competitors. The asymptotic theory based on high-dimensional U-statistic is substantially different from those developed in the literature and is of independent interest.