Detection and estimation of structural change in heavy-tailed sequence. Issue 2 (17th January 2017)

• Record Type: Journal Article
• Authors: Dan, Wang; Pengjiang, Guo; Zhiming, Xia
• Is Part Of: Communications in statistics. Volume 46:Issue 2(2017)
• Page Start: 815
• Page End: 827
• Publication Date: 2017-01-17
• Subjects: Bootstrap test -- change point -- heavy-tailed sequence -- ratio estimation; 62G10 -- 62G05 -- 62F40; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1006780
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this paper, bootstrap detection and ratio estimation are proposed to analysis mean change in heavy-tailed distribution. First, the test statistic is constructed into a ratio form on the CUSUM process. Then, the asymptotic distribution of test statistic is obtained and the consistency of the test is proved. To solve the problem that the null distribution of the test statistic contains unknown tail index, we present a bootstrap approximation method to determine the critical values of the null distribution. We also discuss how to estimate change point based on ratio method. The consistency and rate of convergence for the change-point estimator are established. Finally, the excellent performance of our method is demonstrated through simulations using artificial and real data sets. Especially the simulation results of bootstrap test are better than those of another existing method.