This work proposes a new exchangeability test for random sequence through martingale-based approach. Its main contributions include 1) an additive martingale which is more amenable designing tests by exploiting the Hoeffding-Azuma lemma and 2) different betting functions constructing martingale. By choosing underlying probability density function of p-values as function, it can be shown that, w...

In this paper, we propose a class of monitoring statistics for mean shift in sequence high-dimensional observations. Inspired by the recent U-statistic based retrospective tests developed Wang et al.(2019) and Zhang al.(2020), advance approach to sequential problem developing new adaptive procedure that can detect both dense sparse changes real-time. Unlike where self-normalization was used the...