论文标题
一般双变量位置/比例模型的等渗回归估计值的一些统一结果
Some Unified Results on Isotonic Regression Estimators of Order Restricted Parameters of a General Bivariate Location/Scale Model
论文作者
论文摘要
我们考虑组件的限制位置/比例参数的组件估计$θ_1$和$θ_2$（$θ_1\leqθ_2$）在平方误差损失函数下的一般双变量分布。为了找到比最佳位置/比例估计量（BLEE/BSEE）的改进为$θ_1$和$θ_2$，我们研究了适合位置/比例估算器（LEE/SEE）的等渗回归，为$θ_1$和$θ_2$和$θ_2$。令$ \ mathcal {d} _ {1，ν} $和$ \ Mathcal {d} _ {2，β} $分别表示合适的类别回归估计值$θ_1$和$θ_2$。在平方错误损耗函数下，我们表征了类$ \ Mathcal {d} _ {1，ν} $和$ \ Mathcal {d} _ {2，β} $的可允许的估计器，并识别主导blee/bsee的估计器，该估计值为$θ_1$和$θ_2$。我们的研究统一并扩展了文献中报道的有关具有独立边缘的特定概率分布的研究。此外，还获得了一些新的有趣的结果。还认为一项仿真研究可以比较各种估计器的风险性能。
We consider component-wise estimation of order restricted location/scale parameters $θ_1$ and $θ_2$ ($θ_1\leq θ_2$) 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 $\mathcal{D}_{1,ν}$ and $\mathcal{D}_{2,β}$ 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 $\mathcal{D}_{1,ν}$ and $\mathcal{D}_{2,β}$, 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.
