Inadmissibility of Equivariant Estimators of Order Restricted Location/Scale Parameters of a General Bivariate Distribution Under General Loss function And Their Improvements

We consider equivariant estimation of location/scale parameters of a general bivariate distribution, under quite general conditions on underlying distributions and the loss function, when it is known apriori that these parameters satisfy a order restriction. This problem is broadly studied in the literature for specific probability models having independent marginals and specific loss functions. In most of these studies, sufficient conditions for inadmissibility of best location/scale equivariant estimators are provided. This paper generalizes these results by considering a quite general bivariate model and a quite general loss function. We provide sufficient conditions for inadmissibility of any location/scale equivariant estimator under general probability model (statistical dependent) and general loss function. We also provide some applications of the results obtained in this paper to specific probability models and loss functions that are not studied in the literature.