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Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates

机译:协变量中具有测量误差的嵌套误差线性回归模型下小面积均值的经验贝叶斯估计

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Previously, small area estimation under a nested error linear regression model was studied with area level covariates subject to measurement error. However, the information on observed covariates was not used in finding the Bayes predictor of a small area mean. In this paper, we first derive the fully efficient Bayes predictor by utilizing all the available data. We then estimate the regression and variance component parameters in the model to get an empirical Bayes (EB) predictor and show that the EB predictor is asymptotically optimal. In addition, we employ the jackknife method to obtain an estimator of mean squared prediction error (MSPE) of the EB predictor. Finally, we report the results of a simulation study on the performance of our EB predictor and associated jackknife MSPE estimators. Our results show that the proposed EB predictor can lead to significant gain in efficiency over the previously proposed EB predictor.
机译:以前,在嵌套误差线性回归模型下研究面积估计值存在协方差的小面积估计。但是,有关观察到的协变量的信息并未用于发现小面积均值的贝叶斯预测因子。在本文中,我们首先通过利用所有可用数据来导出完全有效的贝叶斯预测器。然后,我们估计模型中的回归和方差成分参数,以获得经验贝叶斯(EB)预测变量,并证明EB预测变量是渐近最优的。此外,我们采用折刀方法来获得EB预测器的均方预测误差(MSPE)的估计器。最后,我们报告了有关EB预测器和相关折刀MSPE估计器性能的模拟研究结果。我们的结果表明,与先前提出的EB预测器相比,提出的EB预测器可显着提高效率。

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