Data linkage can be used to combine values of the variable of interest from a national survey with values of auxiliary variables obtained from another source, such as a population register, for use in small area estimation. However, linkage errors can induce bias when fitting regression models; moreover, they can create non‐representative outliers in the linked data in addition to the presence of potential representative outliers. In this paper, we adopt a secondary analyst’s point of view, assuming that limited information is available on the linkage process, and develop small area estimators based on linear mixed models and M‐quantile models to accommodate linked data containing a mix of both types of outliers. We illustrate the properties of these small area estimators, as well as estimators of their mean squared error, by means of model‐based and design‐based simulation experiments. We further illustrate the proposed methodology by applying it to linked data from the European Survey on Income and Living Conditions and the Italian integrated archive of economic and demographic micro data in order to obtain estimates of the average equivalised income for labour market areas in central Italy.

中文翻译：

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链接数据的小面积估算

数据链接可用于将国家调查中的目标变量的值与从其他来源（例如人口登记册）获得的辅助变量的值结合起来，以用于小面积估算。但是，在拟合回归模型时，链接错误会导致偏差。此外，除了存在潜在的代表性异常值外，他们还可以在链接数据中创建非代表性异常值。在本文中，我们假设二级分析者的观点是有限的，但仍基于关联过程，并基于线性混合模型和M分位数模型来开发小面积估计量，以容纳包含两种类型的混合数据的关联数据离群值。我们将说明这些小面积估算器的性质以及均方误差的估算器，通过基于模型和基于设计的仿真实验。我们通过将其应用于欧洲收入和生活状况调查以及意大利经济和人口微观数据综合档案库的链接数据，来进一步说明所提出的方法，以便获得意大利中部劳动力市场地区平均平均收入的估计值。