Random weighting estimation of stable exponent |
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Authors: | Gaoge Hu Shesheng Gao Yongmin Zhong Chengfan Gu |
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Affiliation: | 1. School of Automatics, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China 2. School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora, VIC, 3083, Australia 3. School of Materials Science and Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia
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Abstract: | This paper presents a new random weighting method to estimation of the stable exponent. Assume that $X_1, X_2, ldots ,X_n$ is a sequence of independent and identically distributed random variables with $alpha $ -stable distribution G, where $alpha in (0,2]$ is the stable exponent. Denote the empirical distribution function of G by $G_n$ and the random weighting estimation of $G_n$ by $H_n$ . An empirical distribution function $widetilde{F}_n$ with U-statistic structure is defined based on the sum-preserving property of stable random variables. By minimizing the Cramer-von-Mises distance between $H_n$ and ${widetilde{F}}_n$ , the random weighting estimation of $alpha $ is constructed in the sense of the minimum distance. The strong consistency and asymptotic normality of the random weighting estimation are also rigorously proved. Experimental results demonstrate that the proposed random weighting method can effectively estimate the stable exponent, resulting in higher estimation accuracy than the Zolotarev, Press, Fan and maximum likelihood methods. |
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