In this article, we propose a framework for small area estimation with multiply imputed survey data. Many statistical surveys suffer from (a) high nonresponse rates due to sensitive questions and response burden and (b) too small sample sizes to allow for reliable estimates on (unplanned) disaggregated levels due to budget constraints. One way to deal with missing values is to replace them by several plausible/imputed values based on a model. Small area estimation, such as the model by Fay and Herriot, is applied to estimate regionally disaggregated indicators when direct estimates are imprecise. The framework presented tackles simultaneously multiply imputed values and imprecise direct estimates. In particular, we extend the general class of transformed Fay-Herriot models to account for the additional uncertainty from multiple imputation. We derive three special cases of the Fay-Herriot model with particular transformations and provide point and mean squared error estimators. Depending on the case, the mean squared error is estimated by analytic solutions or resampling methods. Comprehensive simulations in a controlled environment show that the proposed methodology leads to reliable and precise results in terms of bias and mean squared error. The methodology is illustrated by a real data example using European wealth data.

中文翻译：

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具有多重估算调查数据的小区域


在本文中，我们提出了一个利用多重估算调查数据进行小区域估计的框架。许多统计调查都面临以下问题：(a) 由于敏感问题和答复负担导致不答复率较高；(b) 由于预算限制，样本量太小，无法对（计划外）分类水平进行可靠估计。处理缺失值的一种方法是用基于模型的几个合理/估算值来替换它们。当直接估计不精确时，小区域估计（例如 Fay 和 Herriot 的模型）可用于估计区域分类指标。该框架提出的解决方案同时解决了估算值的乘法和不精确的直接估计。特别是，我们扩展了转换后的 Fay-Herriot 模型的一般类别，以解释多重插补带来的额外不确定性。我们通过特定变换推导出 Fay-Herriot 模型的三个特殊情况，并提供点和均方误差估计器。根据情况，均方误差通过解析解或重采样方法来估计。受控环境中的综合模拟表明，所提出的方法在偏差和均方误差方面产生了可靠且精确的结果。该方法通过使用欧洲财富数据的真实数据示例进行说明。