We propose a method for the detection of a change point in a sequence of distributions, which are available through a large number of observations at each . Under the null hypothesis, the distributions are equal. Under the alternative hypothesis, there is a change point , such that for and some unknown distribution G, which is not equal to . 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.
This research was partially supported by NSF Grant DMS–1914882.
We thank two referees for posing substantive questions and providing useful advice, which have lead to a much improved paper.
"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