A Note on the Hodges–Lehmann Estimator and the Logistic Distribution

ABSTRACT

It is well known that the Hodges–Lehmann estimator is asymptotically efficient for the location parameter of the logistic distribution. In this article we give a simple and direct proof that this property also characterizes the logistic between all the symmetric location distributions under mild conditions. Using pseudolikelihood, we also show how to find from the Hodges–Lehmann estimator an asymptotically efficient estimator of the scale parameter of the logistic distribution.

Keywords:

• Asymptotically efficient estimator
• Characterization of distributions
• Location and scale models
• Pseudolikelihood
• Symmetric location models

Mathematics Subject Classification:

• Primary 62E10
• Secondary 62F12

Acknowledgments

This research was partially supported by grant BFM2003-04039 from the Department of Education of Spain. The authors thank the referee for his/her valuable comments and suggestions.