A unified study for estimation of order restricted location/scale parameters under the generalized Pitman nearness criterion

TL;DR

This paper develops general methods for improving estimators of order-restricted location and scale parameters under the generalized Pitman nearness criterion, with applications to specific models and simulation comparisons.

Contribution

It introduces new theoretical results for improving estimators under GPN for order-restricted parameters, applicable to various models.

Findings

Improved estimators outperform unrestricted ones under GPN.

Applications demonstrate practical usefulness of the theoretical results.

Simulation shows better performance of proposed estimators.

Abstract

We consider component-wise estimation of order restricted location/scale parameters of a general bivariate location/scale distribution under the generalized Pitman nearness criterion (GPN). We develop some general results that, in many situations, are useful in finding improvements over location/scale equivariant estimators. In particular, under certain conditions, these general results provide improvements over the unrestricted Pitman nearest location/scale equivariant estimators and restricted maximum likelihood estimators. The usefulness of the obtained results is illustrated through their applications to specific probability models. A simulation study has been considered to compare how well different estimators perform under the GPN criterion with a specific loss function.