MONITORING FOR A CHANGE POINT IN A SEQUENCE OF DISTRIBUTIONS
MONITORING FOR A CHANGE POINT IN A SEQUENCE OF DISTRIBUTIONS
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DOI：
10.1214/20-aos2036
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发表时间：
2021-08-01
影响因子：
4.5
通讯作者：
Wang, Shixuan
中科院分区：
文献类型：
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作者：
Horvath, Lajos;Kokoszka, Piotr;Wang, Shixuan
我们提出了一种检测分布序列{F-i}中变化点的方法，这些分布可以通过在每个i >= 1处的大量观测得到。在零假设下，分布F-i相等。在备择假设下，存在一个变化点i* > 1，使得对于i >= i*, F-i = G，并且存在一个未知分布G，不等于F-1。如果存在变化点，则变化点是未知的，并且潜在变化点前后的分布是未知的。当新数据到达时，依次做出关于变更点是否存在的决定。在每一次i，观测的计数N，可以增加到无穷大。检测过程是基于Wasserstein距离的加权版本。建立了它的渐近和有限样本有效性。它的表现可以用标准普尔500指数成份股的回报率来说明。
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 >= 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 >= 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.