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，大数据本身可提供小区域估计值。但这些估计值通常受到大数据固有覆盖偏差和测量误差偏差的影响。然而，若存在同一目标变量的概率调查，可将调查数据作为训练数据集，开发算法以插补大数据缺失数据并修正测量误差。本文提出一种基于kNN算法的插补方法，该算法经过校准，能够渐进设计无偏地估计全国总量，并阐明利用训练数据集估计插补偏差的方法，以及采用固定渐近自助法估计小区域混合估计量方差的方法。我们使用公开数据集展示本文方法，并将混合估计量的准确性与精度与Fay-Harriot（FH）估计量进行比较。最后，通过数值实验检验联结模型中辅助变量存在覆盖不足误差时FH估计量的准确性与精度。