Testing Exchangeability With Martingale for Change-Point Detection
2021 ◽
Vol 12
(2)
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pp. 1-20
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.
2014 ◽
Vol 58
(3)
◽
pp. 488-493
Keyword(s):
2008 ◽
Vol 128
(4)
◽
pp. 583-592
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Keyword(s):
Keyword(s):