Improved estimation of the positive powers ordered restricted standard deviation of two normal populations

TL;DR

This paper develops improved estimators for the positive power of ordered restricted standard deviations of two normal populations, enhancing estimation accuracy under various loss functions through theoretical and simulation analyses.

Contribution

It introduces new estimators and a class of improved estimators, including a generalized Bayes estimator, for better estimation under restrictions and multiple loss functions.

Findings

Proposed estimators outperform existing methods in simulations.

Boundary estimator identified as a generalized Bayes estimator.

Real data analysis confirms practical effectiveness.

Abstract

The present manuscript is concerned with component-wise estimation of the positive power of ordered restricted standard deviation of two normal populations with certain restrictions on the means. We propose several improved estimators under a general scale invariant bowl-shaped loss function. Also, we proposed a class of improved estimators. It has been shown that the boundary estimator of this class is a generalized Bayes. As an application, the improved estimators are obtained with respect to quadratic loss, entropy loss, and a symmetric loss function. We have conducted extensive Monte Carlo simulations to study and compare the risk performance of the proposed estimators. Finally, a real life data analysis is given to illustrate our findings.