Small data estimation for binary variables with big data: A comparison of calibrated nearest neighbour and hierarchical Bayes methods of estimation

Abstract

A recent application in machine learning has introduced a novel approach, complemented by big data sources, aimed at providing precise estimates for small geographical areas. This method employs a dual strategy: (a) hybrid estimation, involving the integration of big data sources with imputed values derived from $K$ nearest neighbours (KNN) to address missing target variable values from the big data source; and (b) calibration of the collective sum of small area estimates to an independent yet efficient national total. Evaluating its efficacy using simulated data from the 2016 Australian population census, the calibrated KNN (CKNN) method demonstrated superior performance compared to the Fay-Herriot method based on area-level covariates.

This paper enhances the comparative analysis by contrasting the CKNN method with a hierarchical Bayes method using the logit-normal model (LN) relevant for binary data. Broadly speaking, the LN method can be viewed as the Bayesian equivalent of Battese-Harter-Fuller (BHF) method, which incorporates unit-level covariates. Our results demonstrate the CKNN method’s superiority over the LN method. However, the application of hybrid estimation to the LN method significantly diminishes this superiority. Although CKNN estimates maintain better precision, they are not as accurate as the estimates from the hybridized LN method.