Sumca: simple, unified, Monte‐Carlo‐assisted approach to second‐order unbiased mean‐squared prediction error estimation
Sumca: simple, unified, Monte‐Carlo‐assisted approach to second‐order unbiased mean‐squared prediction error estimation
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Sumca：简单、统一、蒙特卡罗辅助的二阶无偏均方预测误差估计方法
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发表时间：
2020
期刊：
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通讯作者：
M. Torabi
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作者：
Jiming Jiang;M. Torabi
我们提出了一个简单的，统一的，蒙特卡罗辅助方法（称为“Sumca”）的二阶无偏估计的均方预测误差（MSPE）的小区域预测。所提出的MSPE估计量易于推导，表达式简单，适用于广泛的预测量，包括传统的经验最佳线性无偏预测量、经验最佳预测量和模型选择后的经验最佳线性无偏预测量以及经验最佳预测量。此外，所提出的MSPE估计量的首项保证为正，低阶项对应于偏差校正，其可以通过Monte Carlo方法进行评估。与用于产生二阶无偏MSPE估计量的其他基于蒙特卡罗的方法（例如双重自举和蒙特卡罗刀切法）相比，蒙特卡罗评估的计算负担要小得多。Sumca估计器也有一个很好的稳定性特性。理论和实证结果证明了Sumca估计的性质和优点。
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.