Window-Limited CUSUM for Sequential Change Detection

TL;DR

This paper introduces the Window-Limited CUSUM, a new sequential change detection method that efficiently combines estimation and detection, achieving asymptotic optimality with faster computation.

Contribution

It proposes a novel joint detection/estimation scheme that optimally balances window size and computational efficiency for parametric change detection.

Findings

Achieves first-order asymptotic optimality as average run length increases.

Offers faster recursive computation compared to existing methods.

Numerical simulations confirm theoretical advantages.

Abstract

We study the parametric online changepoint detection problem, where the underlying distribution of the streaming data changes from a known distribution to an alternative that is of a known parametric form but with unknown parameters. We propose a joint detection/estimation scheme, which we call Window-Limited CUSUM, that combines the cumulative sum (CUSUM) test with a sliding window-based consistent estimate of the post-change parameters. We characterize the optimal choice of the window size and show that the Window-Limited CUSUM enjoys first-order asymptotic optimality as average run length approaches infinity under the optimal choice of window length. Compared to existing schemes with similar asymptotic optimality properties, our test can be much faster computed because it can recursively update the CUSUM statistic by employing the estimate of the post-change parameters. A parallel variant is also proposed that facilitates the practical implementation of the test. Numerical simulations corroborate our theoretical findings.