Asymptotic Distribution of the Delay Time in Page's Sequential Procedure

TL;DR

This paper analyzes the asymptotic distribution of the stopping time in Page's CUSUM procedure, demonstrating its advantages over ordinary CUSUM in detecting late changes through theoretical results and simulations.

Contribution

It extends existing results on the asymptotic normality of CUSUM stopping times by specifically characterizing Page's procedure and comparing its performance to ordinary CUSUM.

Findings

Page CUSUM has superior detection in late change scenarios.

Theoretical asymptotic distributions are derived for Page's stopping times.

Simulations confirm the advantages of Page CUSUM over ordinary CUSUM.

Abstract

In this paper the asymptotic distribution of the stopping time in Page's sequential cumulative sum (CUSUM) procedure is presented. Page as well as ordinary cumulative sums are considered as detectors for changes in the mean of observations satisfying a weak invariance principle. The main results on the stopping times derived from these detectors extend a series of results on the asymptotic normality of stopping times of CUSUM-type procedures. In particular the results quantify the superiority of the Page CUSUM procedure to ordinary CUSUM procedures in late change scenarios. The theoretical results are illustrated by a small simulation study, including a comparison of the performance of ordinary and Page CUSUM detectors.