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


  • 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.

published proceedings


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