Some Unified Results on Isotonic Regression Estimators of Order Restricted Parameters of a General Bivariate Location/Scale Model
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We consider component-wise estimation of order restricted location/scale parameters θ_1 and θ_2 (θ_1≤θ_2) of a general bivariate distribution under the squared error loss function. To find improvements over the best location/scale equivariant estimators (BLEE/BSEE) of θ_1 and θ_2, we study isotonic regression of suitable location/scale equivariant estimators (LEE/SEE) of θ_1 and θ_2 with general weights. Let 𝒟_1,ν and 𝒟_2,β denote suitable classes of isotonic regression estimators of θ_1 and θ_2, respectively. Under the squared error loss function, we characterize admissible estimators within classes 𝒟_1,ν and 𝒟_2,β, and identify estimators that dominate the BLEE/BSEE of θ_1 and θ_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 also considered to compare the risk performances of various estimators.
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