to Sumca: Simple, Unified, Monte-Carlo Assisted Approach to Second-order Unbiased MSPE Estimation
to Sumca: Simple, Unified, Monte-Carlo Assisted Approach to Second-order Unbiased MSPE Estimation
复制标题
to Sumca：简单、统一、蒙特卡罗辅助的二阶无偏 MSPE 估计方法
DOI：
--
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
M. Torabi
中科院分区：
文献类型：
--
作者：
Jiming Jiang;M. Torabi
我们提出了一种简单、统一的蒙特卡罗辅助（Sumca）方法来对小区域预测器的均方预测误差（MSPE）进行二阶无偏估计。所提出的 MSPE 估计器易于推导，具有简单的表达式，并且适用于广泛的预测器，包括传统的经验最佳线性无偏预测器（EBLUP）、经验最佳预测器（EBP）以及作为特殊情况的后模型选择 EBLUP 和 EBP。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，可以通过蒙特卡罗方法进行评估。与其他用于生成二阶无偏 MSPE 估计量的基于蒙特卡罗的方法（例如双引导法和蒙特卡罗折刀法）相比，蒙特卡罗评估的计算负担要轻得多。 Sumca 估计器还具有良好的稳定性功能。理论和实证结果证明了 Sumca 估计器的特性和优点。
We propose a simple, unified, Monte-Carlo assisted (Sumca) approach to secondorder unbiased estimation of mean squared prediction error (MSPE) of a small area predictor. The proposed MSPE estimator 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 (EBLUP), empirical best predictor (EBP), and post model selection EBLUP and EBP as special cases. Furthermore, the leading term of the proposed MSPE estimator 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 lesser, compared to other Monte-Carlo based methods that have been used for producing second-order unbiased MSPE estimators, such as 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.