The method of moments ratio estimator for the tail shape parameter Academic Article

abstract

• The so-called Hill estimator for the shape parameter of the tail distribution is known to be downwardly biased. The Hill estimator is a moment estimator, based on the first conditional moment of the highest logarithmically transformed data. We propose a new estimator for the tail index based on the ratio of the second to the first conditional moment. This estimator has a smaller bias than the Hill estimator. We provide simulation results that demonstrate a sizable reduction in bias when is large, while the MSE is moderated as well. The new estimator is applied to stock return data in order to resolve a long standing issue in economics. Copyright 1996 by Marcel Dekker, Inc.

authors

• Jansen, Dennis

published proceedings

• COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

author list (cited authors)

• Danielsson, J., Jansen, D. W., & deVries, C. G.

citation count

• 36

complete list of authors

• Danielsson, J||Jansen, DW||deVries, CG

publication date

• January 1996

publisher

• Taylor & Francis  Publisher

published in

• Communications in Statistics: Theory and Methods  Journal

keywords

• Bias
• Hill Estimator
• Method Of Moments

Digital Object Identifier (DOI)

• 10.1080/03610929608831727

start page

• 711

end page

• 720

volume

• 25

issue

• 4

URL

• http://dx.doi.org/10.1080/03610929608831727