Consistency of a range of penalised cost approaches for detecting multiple changepoints

Zheng, Chao, Eckley, Idris and Fearnhead, Paul (2022) Consistency of a range of penalised cost approaches for detecting multiple changepoints. Electronic Journal of Statistics, 16 (2), 4497-4546. (doi:10.1214/22-EJS2048).

Record type: Article

Abstract

A common approach to detect multiple changepoints is to minimise a measure of data fit plus a penalty that is linear in the number of changepoints. This paper shows that the general finite sample behaviour of such a method can be related to its behaviour when analysing data with either none or one changepoint. This property results in simpler conditions for verifying whether the method will consistently estimate the number and locations of the changepoints. We apply and demonstrate the usefulness of these simple conditions for a range of changepoint problems. Our new results include a weaker requirement on the choice of penalty to have consistency in a change-in-slope model; and the first results for the accuracy of recently-proposed methods for detecting spikes.

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e-pub ahead of print date: 30 August 2022

Published date: 30 August 2022

Additional Information: Funding Information: arXiv: 1911.01716 ∗The authors acknowledge the financial support of the EPSRC and Lancaster University via grant EP/N031938/1. Publisher Copyright: © 2022, Institute of Mathematical Statistics. All rights reserved.

Keywords: Change-point detection„ consistency, changes in slope, local region condition, spike plus exponential decay