Functional Mixed Effects Model for Small Area Estimation.
Functional Mixed Effects Model for Small Area Estimation.
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小面积估计的函数混合效应模型。
DOI：
10.1111/sjos.12218
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Zhong,Ping-Shou
中科院分区：
文献类型：
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作者：
Maiti,Tapabrata;Sinha,Samiran;Zhong,Ping-Shou
函数数据分析因其处理高维和复杂数据结构的能力而成为一个重要的研究领域。然而，线性混合效应模型的发展受到限制，特别是小区域估计。线性混合效应模型是小区域估计的支柱。在本文中，我们考虑区域级数据并拟合变系数线性混合效应模型，其中变系数通过 B 样条进行半参数建模。我们提出了一种估计固定效应参数的方法，并考虑可以使用标准软件实现的随机效应预测。为了测量预测不确定性，我们推导了均方误差的解析表达式，并提出了估计均方误差的方法。该过程通过真实数据示例进行说明，并通过有限样本模拟研究判断该方法的操作特性。
Functional data analysis has become an important area of research because of its ability of handling high‐dimensional and complex data structures. However, the development is limited in the context of linear mixed effect models and, in particular, for small area estimation. The linear mixed effect models are the backbone of small area estimation. In this article, we consider area‐level data and fit a varying coefficient linear mixed effect model where the varying coefficients are semiparametrically modelled via B‐splines. We propose a method of estimating the fixed effect parameters and consider prediction of random effects that can be implemented using a standard software. For measuring prediction uncertainties, we derive an analytical expression for the mean squared errors and propose a method of estimating the mean squared errors. The procedure is illustrated via a real data example, and operating characteristics of the method are judged using finite sample simulation studies.