A unified study for estimation of order restricted parameters of a general bivariate model under the generalized Pitman nearness criterion

We consider component-wise estimation of order-restricted location/scale parameters of a general bivariate location/scale probability distribution under the Generalized Pitman Nearness (GPN) criterion, with a general loss function. In contrast to earlier studies on the same theme, that were mainly focused to specific probability distributions having independent components (marginals), we consider a general bivariate location/scale model and unify various studies made in the literature by developing some general results. These results are useful in finding improvements over arbitrary location/scale equivariant estimators, satisfying certain conditions, under the GPN criterion. In particular, under certain conditions, our results provide improvements over unrestricted Pitman nearest location/scale equivariant estimators and restricted maximum likelihood estimators. We illustrate the usefulness of these results through their applications to specific probability models. Additionally, we conduct a simulation study to compare the performances of different estimators under the GPN criterion with a specific loss function. Furthermore, we provide a real-life data analysis to demonstrate implementation of proposed estimators.