Inference in high-dimensional online changepoint detection

TL;DR

This paper develops new methods for inference in high-dimensional online changepoint detection, providing confidence intervals for changepoints and identifying affected coordinates with controlled error, validated through simulations and real data.

Contribution

It introduces an online algorithm for constructing confidence intervals and support estimation in high-dimensional changepoint detection, with theoretical guarantees and practical validation.

Findings

Confidence intervals with guaranteed coverage are produced.

Support estimation controls false positives and negatives.

Method performs well in simulations and real data applications.

Abstract

We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulations confirm the effectiveness of our methodology, and we also illustrate its applicability on the US excess deaths data from 2017--2020.