We consider component-wise estimation of order restricted location/scale parameters \(\theta _1\) and \(\theta _2\) ( \(\theta _1\le \theta _2\) ) of a general bivariate distribution under the squared error loss function. Motivated by the fact that the isotonic regression of the unrestricted best location/scale equivariant estimators (BLEE/BSEE) or the isotonic regression of the unrestricted maximum likelihood estimators (MLE), of \(\theta _1\) and \(\theta _2\) may not necessarily dominate the unrestricted BLEE/BSEE or the unrestricted MLE of \(\theta _1\) and \(\theta _2\) , to find improvements over the best location/scale equivariant estimators (BLEE/BSEE) of \(\theta _1\) and \(\theta _2\) , we study isotonic regression of suitably chosen location/scale equivariant estimators (LEE/SEE) of \(\theta _1\) and \(\theta _2\) with general weights. Let \({\mathcal {D}}_{1,\nu }\) and \({\mathcal {D}}_{2,\beta }\) denote suitable classes of isotonic regression estimators of \(\theta _1\) and \(\theta _2\) , respectively. Under the squared error loss function, we characterize admissible estimators within classes \({\mathcal {D}}_{1,\nu }\) and \({\mathcal {D}}_{2,\beta }\) , and identify estimators that dominate the BLEE/BSEE of \(\theta _1\) and \(\theta _2\) . Our study unifies and extends several studies reported in the literature for specific probability distributions having independent marginals. Additionally, some new and interesting results are obtained. A simulation study is considered to compare the risk performances of various estimators. A real-life data analysis is also provided to demonstrate the utility of the findings.
