Estimating the scale parameters of several exponential distributions under order restriction

TL;DR

This paper investigates the estimation of ordered exponential distribution scale parameters under the linex loss, proposing improved estimators and demonstrating the inadmissibility of the restricted maximum likelihood estimator through theoretical analysis and simulations.

Contribution

It introduces a class of equivariant estimators for ordered exponential parameters and establishes conditions for their improvement over traditional estimators.

Findings

Proposed estimators outperform usual estimators under certain conditions.

Restricted maximum likelihood estimator is shown to be inadmissible.

Simulation results confirm the theoretical risk improvements.

Abstract

In the present work, we have investigated the problem of estimating parameters of several exponential distributions with ordered scale parameters under the linex loss function. We have considered estimating ordered scale parameters when the location parameters are known and unknown. For every case, we consider a class of equivariant estimators, and sufficient condition is obtained under which this class of estimators improves upon the usual estimator. Using this result, we have shown that the restricted maximum likelihood estimator is inadmissible. Finally, for every case, we conduct a simulation study to compare the risk performance of the proposed estimators.