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Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data

Published online by Cambridge University Press:  17 April 2015

Vytaras Brazauskas  and
Robert Serfling
Vytaras Brazauskas
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201, USA. E-mail: vytaras@uwm.edu
Robert Serfling
Affiliation:
Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75083-0688, USA. E-mail: serfling@utdallas.edu
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Abstract

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Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 2 , November 2003 , pp. 365 - 381
Copyright
Copyright © ASTIN Bulletin 2003

Footnotes

1

Supported by a grant from the Actuarial Education and Research Fund.

2

Supported by grants from the Casualty Actuarial Society and Society of Actuaries, with administrative support from the Actuarial Education and Research Fund, and by NSF Grant DMS-0103698.

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