Consistency of change point estimators for symmetrical stable distribution with parameters shift |
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作者单位: | 1,2 |
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摘 要: | Assume that the characteristic indexαof stable distribution satisfies 1<α<2,and that the distribution is symmetrical about its mean.We consider the change point estimators for stable distribution withαor scale parameterβshift.For the one case that mean is a known constant,ifαorβchanges,then density function will change too.To this end,we suppose the kernel estimation for a change point.For the other case that mean is an unknown constant,we suppose to apply empirical characteristic function to estimate the change-point location.In the two cases,we consider the consistency and strong convergence rate of estimators.Furthermore,we consider the mean shift case.If mean changes,then corresponding characteristic function will change too.To this end,we also apply empirical characteristic function to estimate change point.We obtain the similar convergence rate.Finally,we consider its application on the detection of mean shift in financial market.
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收稿时间: | 24 October 2006 |
修稿时间: | 16 November 2007 |
Consistency of change point estimators for symmetrical stable distribution with parameters shift |
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Authors: | XiaoPing Shi BaiQi Miao and ChunLei Ge |
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Affiliation: | (1) Deptartment of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, China;(2) College of Science, Hefei University of Technology, Hefei, 230009, China |
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Abstract: | Assume that the characteristic index α of stable distribution satisfies 1 < α < 2, and that the distribution is symmetrical about its mean. We consider the change point estimators for stable distribution
with α or scale parameter β shift. For the one case that mean is a known constant, if α or β changes, then density function will change too. To this end, we suppose the kernel estimation for a change point. For the
other case that mean is an unknown constant, we suppose to apply empirical characteristic function to estimate the change-point
location. In the two cases, we consider the consistency and strong convergence rate of estimators. Furthermore, we consider
the mean shift case. If mean changes, then corresponding characteristic function will change too. To this end, we also apply
empirical characteristic function to estimate change point. We obtain the similar convergence rate. Finally, we consider its
application on the detection of mean shift in financial market.
This work was supported by the National Natural Science Foundation of China (Grant No. 10471135) and Graduate Innovation Fund
of the University of Science and Technology of China (Grant No. KD2006063) |
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Keywords: | stable distribution change point consistency strong convergence rate |
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