AI 中文总结
本文针对辅助变量含测量误差且来自非传统大数据的小区域估计问题，提出空间测量误差Fay-Herriot模型，经模拟验证后用于西班牙区域气候变化态度估计，可兼顾空间相关性与协变量测量误差以提升估计可靠性。
AI 中文摘要
小区域估计方法结合直接调查估计与基于模型的预测，以生成总体数量的可靠估计。当协变量存在测量误差时（这种情况常发生于辅助信息来自大数据源时），若忽略该测量误差，传统Fay-Herriot模型等标准区域层面方法的表现可能较差，甚至可能产生有偏估计。在Ybarra和Lohr提出的协变量测量误差扩展方法基础上，我们进一步开发该建模框架，纳入区域间的空间依赖性。我们提出一种空间测量误差Fay-Herriot模型，该模型同时考虑协变量测量误差与空间相关性，可在对协变量引入的额外不确定性进行适当调整的同时，实现相关邻域间的信息借用。我们推导了所提模型及其参数估计量的性质，并概述了用于估计所得经验最佳线性无偏预测器均方误差的参数自助法。一项模拟研究在一系列测量误差场景下检验了模型性能。随后将所提方法应用于补充了大数据辅助信息的欧洲社会调查数据，以估计西班牙各区域对气候变化的态度。
英文摘要
Small area estimation methods combine direct survey estimates with model-based predictions to produce reliable estimates of population quantities. When covariates are measured with error, as often occurs when auxiliary information is coming from big data sources, standard area-level approaches such as the traditional Fay-Herriot model can perform poorly if this measurement error is ignored, potentially yielding biased estimates. Building on the extension proposed by Ybarra and Lohr to account for measurement error in covariates, we further develop this modelling framework by incorporating spatial dependence between areas. We propose a spatial measurement error Fay-Herriot model that jointly accounts for covariate measurement error and spatial correlation, enabling information borrowing across relevant neighbouring areas while properly adjusting for the additional uncertainty introduced by the covariates. We derive the properties of the proposed model and its parameter estimators and outline a parametric bootstrap procedure for estimating the mean squared error of the resulting empirical best linear unbiased predictor. A simulation study examines model performance under a range of measurement error scenarios. The proposed approach is then applied to European Social Survey data, supplemented with big data auxiliary information, to estimate regional attitudes towards climate change in Spain.
Comments36 pages, 15 figures
