On conditional prediction errors in mixed models with application to small area estimation
On conditional prediction errors in mixed models with application to small area estimation
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混合模型条件预测误差及其在小区域估计中的应用
DOI：
10.1016/j.jmva.2016.02.009
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发表时间：
2016
影响因子：
1.6
通讯作者：
T.
中科院分区：
文献类型：
--
作者：
Sugasawa;S and Kubokawa;T.
混合模型中的经验贝叶斯估计在提高小区域均值预测精度的意义上对小区域估计是有用的，人们想知道基于数据的经验贝叶斯估计的预测误差。本文研究的是混合模型中的条件预测误差，而不是传统的无条件预测误差。在具有二次方差函数的自然指数族的混合模型中，在远离正态分布的情况下，条件预测误差和无条件预测误差之间的差异是显著的。特别是对于二项-贝塔混合模型和泊松-伽马混合模型，条件预测误差的先导项分别是小区域内直接估计的二次凹函数和递增函数，而相应的无条件预测误差的先导项是常量。文中还推导了条件预测误差的二阶无偏估计，并通过仿真和实证研究检验了它们的性能。
The empirical Bayes estimators in mixed models are useful for small area estimation in the sense of increasing precision of prediction for small area means, and one wants to know the prediction errors of the empirical Bayes estimators based on the data. This paper is concerned with conditional prediction errors in the mixed models instead of conventional unconditional prediction errors. In the mixed models based on natural exponential families with quadratic variance functions, it is shown that the difference between the conditional and unconditional prediction errors is significant under distributions far from normality. Especially for the binomial–beta mixed and the Poisson–gamma mixed models, the leading terms in the conditional prediction errors are, respectively, a quadratic concave function and an increasing function of the direct estimate in the small area, while the corresponding leading terms in the unconditional prediction errors are constants. Second-order unbiased estimators of the conditional prediction errors are also derived and their performances are examined through simulation and empirical studies.