Estimation of Order Restricted Location/Scale Parameters of a General Bivariate Distribution Under General Loss function: Some Unified results

TL;DR

This paper develops unified methods for estimating ordered location and scale parameters in bivariate distributions, providing theoretical improvements, simulations, and real data applications to demonstrate their effectiveness.

Contribution

It offers a unified framework for improving equivariant estimators of ordered parameters under general conditions, extending existing results.

Findings

Unified conditions for estimator improvement

Simulation results show risk reductions in normal and gamma models

Real data analysis confirms practical applicability

Abstract

We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various results in the literature dealing with sufficient conditions for finding improvments over arbitrary location/scale equivariant estimators. The usefulness of these results is illustrated through various examples. A simulation study is considered to compare risk performances of various estimators under bivariate normal and independent gamma probability models. A real-life data analysis is also performed to demonstrate applicability of the derived results.