Sequential change detection based on universal compression algorithms

The application of universal source coding algorithms to the problem of classification was initiated by Ziv and has been extended to other problems in statistics such as order estimation. In spite of the large literature, these studies have been limited to problems with fixed number of samples. In this paper we study the application of universal source coding to the problem of sequential hypothesis testing and sequential change detection. Algorithms are proposed which are inspired by Waldpsilas Sequential Probability Ratio Test (SPRT) and Pagepsilas Cumulative Sum Test (CUSUM) for these problems respectively. Performance of the proposed algorithms are studied in the asymptotic regime to demonstrate their effectiveness.