Sequential Change Detection through Empirical Distribution and Universal Codes

TL;DR

This paper proposes a modified CUSUM change detection method that uses empirical distributions for both pre- and post-change scenarios, demonstrating its asymptotic optimality.

Contribution

It introduces a new CUSUM test that handles unknown pre-change distributions using empirical estimates, extending previous methods that only addressed post-change unknowns.

Findings

Proves asymptotic optimality of the modified CUSUM test.

Analyzes characteristics of the empirical distribution-based change detection.

Extends change detection theory to cases with unknown pre-change distributions.

Abstract

Universal compression algorithms have been studied in the past for sequential change detection, where they have been used to estimate the post-change distribution in the modified version of the Cumulative Sum (CUSUM) Test. In this paper, we introduce a modified CUSUM test where the pre-change distribution is also unknown and an empirical version of the pre-change distribution is used to implement the algorithm. We present a study of various characteristics of this modified CUSUM Test and then prove its asymptotic optimality.