Monitoring for a change point in a sequence of distributions
Horváth, L., Kokoszka, P. and Wang, S.
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1214/20-AOS2036 Abstract/SummaryWe 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.
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