Monitoring for a change point in a sequence of distributions
Lajos Horváth, Piotr Kokoszka, Shixuan Wang
The Annals of Statistics · 2021 · Volume 49 · Issue 4
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 i≥1. 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 i≥i∗ 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.
Keywords
62G10, 62G20, 62G30, 62L10, change point detection, Empirical quantile function, sequential monitoring, Wasserstein distance
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