  The problem of estimating location (scale) parameters $\theta_1$ and
$\theta_2$ of two distributions when the ordering between them is known apriori
(say, $\theta_1\leq \theta_2$) has been extensively studied in the literature.
Many of these studies are centered around deriving estimators that dominate the
best location (scale) equivariant estimators, for the unrestricted case, by
exploiting the prior information that $\theta_1 \leq \theta_2$. Several of
these studies consider specific distributions such that the associated random
variables are statistically independent. This paper considers a general
bivariate model and general loss function and unifies various results proved in
the literature. We also consider applications of these results to a bivariate
normal and a Cheriyan and Ramabhadran's bivariate gamma model. A simulation
study is also considered to compare the risk performances of various estimators
under bivariate normal and Cheriyan and Ramabhadran's bivariate gamma models.
