The problem of simultaneous estimation of location/scale parameters $\theta_1$ and $\theta_2$ of a general bivariate location/scale model, when the ordering between the parameters is known apriori (say, $\theta_1\leq \theta_2$), has been considered. We consider isotonic regression estimators based on the best location/scale equivariant estimators (BLEEs/BSEEs) of $\theta_1$ and $\theta_2$ with general weight functions. Let $\mathcal{D}$ denote the corresponding class of isotonic regression estimators of $(\theta_1,\theta_2)$. Under the sum of the weighted squared error loss function, we characterize admissible estimators within the class $\mathcal{D}$, and identify estimators that dominate the BLEE/BSEE of ($\theta_1$,$\theta_2$). Our study unifies several studies reported in the literature for specific probability distributions having independent marginals. We also report a generalized version of the Katz (1963) result on the inadmissibility of certain estimators under a loss function that is weighted sum of general loss functions for component problems. A simulation study is also carried out to validate the findings of the paper.
翻译:考虑过同时估算一个通用双变位置/规模参数($\theta_1美元和$\theta_2美元)的问题。 当参数之间已知的偏差值( 例如, $\theta_ 1\leq\theta_ 2美元) 时, 同时估算一个通用双变位置/规模参数( $_ 1美元 和$\theta_ 2美元) / 标度模型的位置/ 美元。 我们考虑的是基于最佳位置/ 规模等差估计器( lebelEs/ SQFEEs) 的异调回归估计器( $\theta_ 1美元 美元 和 $\theta_ 2美元 美元) 的问题。 在加权平方差损失函数的总和下, 我们考虑的是基于最佳位置/ equal- eq 等差估计器( $_ 1美元 美元 美元 和 $\\ tta_ 2美元 美元) 。 我们的研究在文献中报告的有关异位回归回归估计值的相应估计值的相应测量函数( 19lorimalestalalalalestal ) eximalestalestal dislal dislvial dism realismismism report 。我们还报告了A 总和Simmismlislislismlispalismisbal debalismismismismism repalismismismismismismismismismismismismismisbal debal debal debaldald a a a a s。