A new shift invariant Hill-type estimator for heavy tailed models. (10th July 2012)

• Record Type: Journal Article
• Authors: Cai, Xia; Li, Xiumin
• Is Part Of: International journal of modelling, identification and control. Volume 16:Number 3(2012)
• Page Start: 206
• Page End: 211
• Publication Date: 2012-07-10
• Subjects: extreme value index -- shift and scale invariant -- heavy tail -- Hill estimator; Engineering -- Methodology -- Periodicals; Science -- Methodology -- Periodicals; 001.42
• Languages: English
• ISSNs: 1746-6172

Abstract

In this paper, we build a new Hill-type estimator of extreme value index, which is close to the true value for a class of heavy-tailed models. The new estimator, which is based on the original Hill's estimator and generalised Hill's estimator, depends on a positive parameter. It is invariant for changes in both scale and shift. The simulation studies are presented to show that the new estimator performs well compared to the known ones when γ is between 1/2 and 2/3. Finally, we apply this new method to the logarithmic rate of return in stock market.