Testing exchangeability with martingale for change-point detection
Statistics Theory
2020-07-27 v2 Statistics Theory
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; 2) different betting functions for constructing the additive martingale are studied. 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.
Cite
@article{arxiv.1810.04022,
title = {Testing exchangeability with martingale for change-point detection},
author = {Liang Dai and Mohamed-Rafik Bouguelia},
journal= {arXiv preprint arXiv:1810.04022},
year = {2020}
}