A note on estimation of a shape parameter in a Pareto distribution

Abstract

Considering an estimation problem of a shape parameter in a Pareto distribution under a restriction of a scale parameter, an estimator dominating all the previous estimators is proposed. Especially, under the quadratic loss function, the proposed estimator is shown to be second-order admissible in the class of all modified maximum likelihood estimators.

Keywords:

• Pareto distribution
• restricted parameter space
• second-order admissibility
• shape parameter

AMS 2010 SUBJECT CLASSIFICATIONS:

• 62F10
• 62F12

Acknowledgments

The authors thank anonymous referee for many comments and suggestions, which improved the paper.

Additional information

Funding

This work was partially supported by JSPS KAKENHI [Grant Number JP19K11864].