Computational Statistics

, Volume 25, Issue 1, pp 97–105

A highly efficient L-estimator for the location parameter of the Cauchy distribution

Authors

    • School of Mathematics and StatisticsYunnan University
Original Paper

DOI: 10.1007/s00180-009-0163-y

Cite this article as:
Zhang, J. Comput Stat (2010) 25: 97. doi:10.1007/s00180-009-0163-y

Abstract

The Cauchy distribution is a peculiar distribution due to its heavy tail and the difficulty of estimating its location parameter. It is often cited as an example of the computational failure of the maximum likelihood method of estimation. The method of moment estimation fails and Bayesian estimation is very unstable. A new unbiased L-estimator based on order statistics is proposed, which is not only asymptotically efficient but outperforms existing L-estimators in terms of finite-sample efficiency.

Keywords

Asymptotic efficiencyThe Cramér-Rao lower boundMaximum likelihood estimatorMean square errorOrder statistics

Copyright information

© Springer-Verlag 2009