Empirical Bayesian estimation of location of the Cauchy distribution

Abstract

The Cauchy distribution has a heavy tail so that the estimation of its location becomes complex. An empirical Bayesian estimation of the location for the Cauchy distribution is proposed in this article. The new estimator is not only computationally easy, but also the most efficient estimator, compared with existing estimators in the literature.

Keywords:

• asymptotic efficiency
• Bayesian estimator
• the Cramér-Rao lower bound
• L-estimator
• maximum likelihood estimator

Acknowledgements

This research is supported by the Natural Science Foundation of China (NSFC, Grant No. 1161054). The author thanks a referee for valuable comments and suggestions.