Componentwise Equivariant Estimation of Order Restricted Location and Scale Parameters In Bivariate Models: A Unified Study

The problem of estimating location (scale) parameters of two distributions when the ordering between them is known apriori has been extensively studied in the literature. Many of these studies are centered around deriving estimators that dominate the maximum likelihood estimators and/or best location (scale) equivariant estimators for the unrestricted case, by exploiting the prior information. Several of these studies consider specific distributions such that the associated random variables are statistically independent. In this paper, we consider a general bivariate model and general loss function and unify various results proved in the literature. We also consider applications of these results to various dependent bivariate models (bivariate normal, a bivariate exponential model based on a Morgenstern family copula, a bivariate model due to Cheriyan and Ramabhadran's and Mckay's bivariate gamma model) not studied in the literature. We also apply our results to two bivariate models having independent marginals (exponential-location and power-law distributions) that are already studied in the literature, and obtain the results proved in the literature for these models as a special case of our study.