A new limit result in change point analysis. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Atya, Shrief Prince; Abdel-Ghaly, Abdalla; Ebaid, Rasha
• Is Part Of: Communications in statistics. Volume 52:Issue 1(2023)
• Page Start: 196
• Page End: 207
• Publication Date: 2023-01-02
• Subjects: α-Mixing -- functional central limit theorem -- triangular array; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1910843
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: Change points are abrupt changes in time ordered data. The cumulative sum (CUSUM) test statistic is an important statistic for testing for a change point. In this article, we prove a functional central limit theorem for heterogeneous α -mixing triangular array in D [ 0, 1 ] assuming a Riemann integrable variance function. We investigate the asymptotic behavior of the CUSUM statistic under the null and alternative hypotheses through a simulation.