Random weighting estimation of stable exponent

Gaoge Hu (), Shesheng Gao, Yongmin Zhong and Chengfan Gu

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 4, 468 pages

Abstract: This paper presents a new random weighting method to estimation of the stable exponent. Assume that $$X_1, X_2, \ldots ,X_n$$ X 1 , X 2 , ... , X n is a sequence of independent and identically distributed random variables with $$\alpha $$ α -stable distribution G, where $$\alpha \in (0,2]$$ α ∈ ( 0 , 2 ] is the stable exponent. Denote the empirical distribution function of G by $$G_n$$ G n and the random weighting estimation of $$G_n$$ G n by $$H_n$$ H n . An empirical distribution function $$\widetilde{F}_n$$ 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 $$H_n$$ H n and $${\widetilde{F}}_n$$ F ~ n , the random weighting estimation of $$\alpha $$ α 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. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Stable distribution; Stable exponent; Random weighting estimation; Minimum distance; Strong consistency; Asymptotic normality (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00184-013-0448-6

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