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August 2021 Monitoring for a change point in a sequence of distributions
Lajos Horváth, Piotr Kokoszka, Shixuan Wang
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Ann. Statist. 49(4): 2271-2291 (August 2021). DOI: 10.1214/20-AOS2036

Abstract

We propose a method for the detection of a change point in a sequence {Fi} of distributions, which are available through a large number of observations at each i1. Under the null hypothesis, the distributions Fi are equal. Under the alternative hypothesis, there is a change point i>1, such that Fi=G for ii and some unknown distribution G, which is not equal to F1. The change point, if it exists, is unknown, and the distributions before and after the potential change point are unknown. The decision about the existence of a change point is made sequentially, as new data arrive. At each time i, the count of observations, N, can increase to infinity. The detection procedure is based on a weighted version of the Wasserstein distance. Its asymptotic and finite sample validity is established. Its performance is illustrated by an application to returns on stocks in the S&P 500 index.

Funding Statement

This research was partially supported by NSF Grant DMS–1914882.

Acknowledgments

We thank two referees for posing substantive questions and providing useful advice, which have lead to a much improved paper.

Citation

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Lajos Horváth. Piotr Kokoszka. Shixuan Wang. "Monitoring for a change point in a sequence of distributions." Ann. Statist. 49 (4) 2271 - 2291, August 2021. https://doi.org/10.1214/20-AOS2036

Information

Received: 1 April 2020; Revised: 1 November 2020; Published: August 2021
First available in Project Euclid: 29 September 2021

Digital Object Identifier: 10.1214/20-AOS2036

Subjects:
Primary: 62G30 , 62L10
Secondary: 62G10 , 62G20

Keywords: change point detection , Empirical quantile function , sequential monitoring , Wasserstein distance

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 4 • August 2021
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