Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume 53, Issue 4, Pages 990-998Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.csda.2008.11.015
Keywords
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Funding
- Natural Sciences and Engineering Research Council of Canada
- NSFC [10471135]
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Let {X-n, n >= 1} be an independent sequence with a mean shift. We consider the cumulative sum (CUSUM) estimator of a change point. It is shown that, when the rth moment of X-n is finite, for n >= 1 and r > 1, strong convergence rate of the change point estimator is r o(M(n)/n), for any M(n) satisfying that M(n) up arrow infinity, which has improved the results the literature. Furthermore, it is also shown that the preceding rate is still valid for some dependent or negative associate cases. We also propose an iterative algorithm to search for the location of a change point. A simulation study on a mean shift model with a stable distribution is provided, which demonstrates that the algorithm is efficient. In addition, a real data example is given for illustration. (C) 2008 Elsevier B.V. All rights reserved.
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