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arXiv · 2608.09626

A Spatial Fay-Herriot Model when the Auxiliary Variables are based on Non-traditional Data

Robin Markwitz·Angelo Moretti·Camilla Salvatore
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Abstract

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.

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Robin Markwitz, Angelo Moretti, Camilla Salvatore. 2026-08-10. A Spatial Fay-Herriot Model when the Auxiliary Variables are based on Non-traditional Data. https://arxiv.org/abs/2608.09626

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