Testing Exchangeability With Martingale for Change-Point Detection

Liang Dai and Mohamed-Rafik Bouguelia
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Liang Dai: Halmstad University, Sweden
Mohamed-Rafik Bouguelia: Halmstad University, Sweden

International Journal of Ambient Computing and Intelligence (IJACI), 2021, vol. 12, issue 2, 1-20

Abstract: This work proposes a new exchangeability test for a random sequence through a martingale-based approach. Its main contributions include 1) an additive martingale which is more amenable for designing exchangeability tests by exploiting the Hoeffding-Azuma lemma and 2) different betting functions for constructing the additive martingale. By choosing the underlying probability density function of p-values as a betting function, it can be shown that, when a change-point appears, a satisfying trade-off between the smoothness and expected one-step increment of the martingale sequence can be obtained. An online algorithm based on beta distribution parametrization for constructing this betting function is discussed in detail as well.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:igg:jaci00:v:12:y:2021:i:2:p:1-20

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