2022/07/02 by Naresh Kumar Garg, Neeraj Misra, Garg, Naresh +1
Mathematics · #Statistical Distribution Estimation and Applications #Advanced Statistical Methods and Models #Survey Sampling and Estimation Techniques
paper · pdf · doi:10.48550/arxiv.2207.00771
We consider component-wise estimation of order restricted location/scale parameters θ1 and θ2 (θ1≤ θ2) of a general bivariate distribution under the squared error loss function. To find improvements over the best location/scale equivariant estimators (BLEE/BSEE) of θ1 and θ2, we study isotonic regression of suitable location/scale equivariant estimators (LEE/SEE) of θ1 and θ2 with general weights. Let D1,ν and D2,β denote suitable classes of isotonic regression estimators of θ1 and θ2, respectively. Under the squared error loss function, we characterize admissible estimators within classes D1,ν and D2,β, and identify estimators that dominate the BLEE/BSEE of θ1 and θ2. 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.