Where the response variable in a big data set is consistent with the variable of interest for small area estimation, the big data by itself can provide the estimates for small areas. These estimates are often subject to the coverage and measurement error bias inherited from the big data. However, if a probability survey of the same variable of interest is available, the survey data can be used as a training data set to develop an algorithm to impute for the data missed by the big data and adjust for measurement errors. In this paper, we outline a methodology for such imputations based on an kNN algorithm calibrated to an asymptotically design-unbiased estimate of the national total and illustrate the use of a training data set to estimate the imputation bias and the fixed - asymptotic bootstrap to estimate the variance of the small area hybrid estimator. We illustrate the methodology of this paper using a public use data set and use it to compare the accuracy and precision of our hybrid estimator with the Fay-Harriot (FH) estimator. Finally, we also examine numerically the accuracy and precision of the FH estimator when the auxiliary variables used in the linking models are subject to under-coverage errors

翻译：当大数据集中的响应变量与小区域估计的目标变量一致时，大数据本身即可提供小区域估计值。然而，这些估计往往存在大数据固有的覆盖偏差和测量误差偏差。若同一目标变量的概率调查数据可用，则可将其作为训练数据集，开发一种算法，用于填补大数据遗漏的数据并修正测量误差。本文基于k近邻（kNN）算法，提出一种校准至全国总量渐近设计无偏估计的插补方法框架，并阐述了利用训练数据集估计插补偏差的方法，以及通过固定渐近自助法估计小区域混合估计量方差的策略。我们利用公开数据集演示了本文方法，并将其与Fay-Harriot（FH）估计量进行精度与准确度比较。最后，我们通过数值实验考察了当链接模型中的辅助变量存在覆盖不足误差时，FH估计量的准确度与精度表现。