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arXiv 2403.11276stat.MEstat.AP
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模型误设对小区域估计量的影响

Effects of model misspecification on small area estimators

Yuting Chen, Partha Lahiri, Nicola Salvati

AI总结:

该研究通过蒙特卡洛模拟探究均值结构误设对小区域估计量的影响,发现观测单元层面辅助变量会使OBP表现变差,改用区域层面辅助变量或对应模型可显著提升其性能,且OBP的MSPE随辅助变量样本与总体均值差增大而上升。

摘要:

嵌套误差回归模型常被用于纳入观测单元特定的辅助变量以改进小区域估计。当该模型的均值结构被误设时,经验最优线性无偏预测器(EBLUP)的均方预测误差(MSPE)通常会增大。观测最优预测(OBP)方法已被提出,旨在在MSPE上优于EBLUP。我们开展了一项蒙特卡洛模拟实验,以探究均值结构误设对不同小区域估计量的影响。我们的模拟结果得出了一个意外发现:当使用观测单元层面的辅助变量时,OBP的表现可能非常差;而当在嵌套误差回归模型中使用这些辅助变量的总体均值(区域层面辅助变量)时,或使用对应的区域层面模型时,OBP可得到显著改进。我们的模拟还表明,OBP的MSPE是辅助变量的样本均值与总体均值之差的递增函数。

英文摘要:

Nested error regression models are commonly used to incorporate observational unit specific auxiliary variables to improve small area estimates. When the mean structure of this model is misspecified, there is generally an increase in the mean square prediction error (MSPE) of Empirical Best Linear Unbiased Predictors (EBLUP). Observed Best Prediction (OBP) method has been proposed with the intent to improve on the MSPE over EBLUP. We conduct a Monte Carlo simulation experiment to understand the effect of mispsecification of mean structures on different small area estimators. Our simulation results lead to an unexpected result that OBP may perform very poorly when observational unit level auxiliary variables are used and that OBP can be improved significantly when population means of those auxiliary variables (area level auxiliary variables) are used in the nested error regression model or when a corresponding area level model is used. Our simulation also indicates that the MSPE of OBP in an increasing function of the difference between the sample and population means of the auxiliary variables.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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