Random weighting estimation of stable exponent

This paper presents a new random weighting method to estimation of the stable exponent. Assume that is a sequence of independent and identically distributed random variables with -stable distribution G, where is the stable exponent. Denote the empirical distribution function of G by and the random weighting estimation of by . An empirical distribution function with U-statistic structure is defined based on the sum-preserving property of stable random variables. By minimizing the Cramer-von-Mises distance between and , the random weighting estimation of 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.