An Estimator of Heavy Tail Index through the Generalized Jackknife Methodology

Mathematical Problems in Engineering. 2014;2014 DOI 10.1155/2014/686240

 

Journal Homepage

Journal Title: Mathematical Problems in Engineering

ISSN: 1024-123X (Print); 1563-5147 (Online)

Publisher: Hindawi Publishing Corporation

LCC Subject Category: Technology: Engineering (General). Civil engineering (General) | Science: Mathematics

Country of publisher: Egypt

Language of fulltext: English

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AUTHORS

Weiqi Liu (Institute of Management and Decision, Shanxi University, Taiyuan 030006, China)
Hongwei Xing (School of Business, Shanxi University, Taiyuan 030006, China)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 26 weeks

 

Abstract | Full Text

In practice, sometimes the data can be divided into several blocks but only a few of the largest observations within each block are available to estimate the heavy tail index. To address this problem, we propose a new class of estimators through the Generalized Jackknife methodology based on Qi’s estimator (2010). These estimators are proved to be asymptotically normal under suitable conditions. Compared to Hill’s estimator and Qi’s estimator, our new estimator has better asymptotic efficiency in terms of the minimum mean squared error, for a wide range of the second order shape parameters. For the finite samples, our new estimator still compares favorably to Hill’s estimator and Qi’s estimator, providing stable sample paths as a function of the number of dividing the sample into blocks, smaller estimation bias, and MSE.