, Volume 25, Issue 1, pp 97-105

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

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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.