Monitoring for a change point in a sequence of distributions

Horváth, L., Kokoszka, P. and Wang, S. ORCID: https://orcid.org/0000-0003-2113-5521 (2021) Monitoring for a change point in a sequence of distributions. Annals of Statistics, 49 (4). pp. 2271-2291. ISSN 2168-8966 doi: 10.1214/20-AOS2036

Abstract/Summary

We propose a method for the detection of a change point in a sequence $\{F_i\}$ of distributions, which are available through a large number of observations at each $i \geq 1$. Under the null hypothesis, the distributions $F_i$ are equal. Under the alternative hypothesis, there is a change point $i^* > 1$, such that $F_i = G$ for $i \geq i^*$ and some unknown distribution $G$, which is not equal to $F_1$. 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/93785
Identification Number/DOI	10.1214/20-AOS2036
Refereed	Yes
Divisions	Arts, Humanities and Social Science > School of Politics, Economics and International Relations > Economics
Publisher	Institute of Mathematical Statistics
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