Sequential Change Detection Based on Universal Compression for Markov Sources

Abstract

A universal compression code can act as an estimator for the distribution of a finite alphabet finite-order Markov source. This property of universal codes was exploited by Jacob and Bansal in [5] to propose a modification of the CUSUM test in order to solve the change detection problem when the post-change distribution is not known. The performance of this test was proven to be asymptotically optimal for a memoryless sources and class of sources with memory under Lorden’s minimax formulation. This study was further extended in [9] where performance of the modified CUSUM for an i.i.d. setting under Lai’s criterion involving a constraint on the probability of false alarm within a window (PFAW) was analyzed. In this paper, we introduce a modified version of the window limited CUSUM (WL-CUSUM) test by incorporating strongly universal code. We closely follow the work of Lai [8] in order to prove the asymptotic optimality for the test under the PFAW criterion. We further prove the asymptotic optimality of the modified WL-CUSUM test in the Bayesian setting.