We propose a simple, unified, Monte‐Carlo‐assisted approach (called ‘Sumca’) to second‐order unbiased estimation of the mean‐squared prediction error (MSPE) of a small area predictor. The MSPE estimator proposed is easy to derive, has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor, empirical best predictor and post‐model‐selection empirical best linear unbiased predictor and empirical best predictor as special cases. Furthermore, the leading term of the MSPE estimator proposed is guaranteed positive; the lower order term corresponds to a bias correction, which can be evaluated via a Monte Carlo method. The computational burden for the Monte Carlo evaluation is much less, compared with other Monte‐Carlo‐based methods that have been used for producing second‐order unbiased MSPE estimators, such as the double bootstrap and Monte Carlo jackknife. The Sumca estimator also has a nice stability feature. Theoretical and empirical results demonstrate properties and advantages of the Sumca estimator.

中文翻译：

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Sumca：简单，统一，蒙特卡洛辅助方法进行二阶无偏均方预测误差估计

我们提出了一种简单，统一的蒙特卡洛辅助方法（称为“ Sumca”）来对小面积预测变量的均方预测误差（MSPE）进行二阶无偏估计。提出的MSPE估计量易于导出，表达简单，并适用于广泛的预测变量，包括传统的经验最佳线性无偏预测变量，经验最佳预测和模型选择后经验最佳线性无偏预测变量和经验最佳预测变量。特别案例。此外，所建议的MSPE估计量的首项保证为正；低阶项对应于偏差校正，可以通过蒙特卡洛方法进行评估。蒙特卡洛评估的计算量要少得多，与其他用于生成二阶无偏MSPE估计量的基于蒙特卡洛的方法相比，例如双引导程序和蒙特卡罗折刀。Sumca估算器还具有良好的稳定性。理论和经验结果证明了Sumca估计器的特性和优点。