A calibrated data-driven approach for small area estimation using big data

Where the response variable in a big dataset 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 dataset 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 k-nearest neighbours (kNN) algorithm calibrated to an asymptotically design-unbiased estimate of the national total, and illustrate the use of a training dataset to estimate the imputation bias and the “fixed-k asymptotic” bootstrap to estimate the variance of the small area hybrid estimator. We illustrate the methodology of this paper using a public-use dataset 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 undercoverage errors.