Order preserving property of moment estimators

TL;DR

This paper investigates conditions under which moment estimators preserve stochastic orders, extending previous work on maximum likelihood estimators to include various families like exponential, location, and scale families.

Contribution

It provides new sufficient conditions for moment estimators to preserve stochastic orders across different distribution families.

Findings

Conditions established for one-parameter families

Preservation of stochastic order for exponential family

Results applicable to location and scale families

Abstract

Balakrishnan and Mi [1] considered order preserving property of maximum likelihood estimators. In this paper there are given conditions under which the moment estimators have the property of preserving stochastic orders. There is considered property of preserving for usual stochastic order as well as for likelihood ratio order. Mainly, sufficient conditions are given for one parameter family of distributions and also for exponential family, location family and scale family.