正规变化重尾分布尾部指数的Crovella估计的强相合性

Strong Consistency of Crovella Estimation for the Tail Index of Regular Variation Heavy-Tailed Distribution

正规变化重尾分布的尾部指数的估计方法有很多种,但都不同程度地存在一定的局限性.为此,Crov-ella提出了一种从标度特征方面来估计尾部指数的方法,该方法易于应用,估计结果也比较准确.本文在阐述了该估计方法的具体步骤后,给出了相应的估计量,并证明了该估计量具有强相合性.

The estimation of tail index for regular variation heavy-tailed distributions aroused our concern, many scholars proposed several methods, but all of them have some disadvantages. Crovella presented a new method based on the scaling properties of sums of heavy-tailed randomvariables. It has the advantages of being easy to apply, and of being relatively accurate. In this paper, the estimation presented by Crovella is described, and that the Crovella estimator has strong consistency is proved.