Estimation of small area counts with the benchmarking property

Abstract

Estimation of small area totals makes use of auxiliary variables to borrow strength from related areas through a model. Precision of final small area estimates depends on the validity of such a model. To protect against possible model failures, benchmarking procedures make the sum of small area estimates match a design consistent estimate of the total of a larger area. This is also particularly important for national institutes of statistics to ensure coherence between small area estimates and direct estimates produced at higher level planned domains. In this paper we propose a self-benchmarked estimator of small area totals which is based on a unit level logistic mixed model for a binary response. In particular, we use a plug-in approach and add a constraint to the maximum penalized quasi-likelihood (PQL) procedure considered in Saei and Chambers (Working paper M03/15, Southampton Statistical Sciences Research Institute. University of Southampton, 2003) to accommodate benchmarking. An analytic estimator for the mean squared error of the final small area estimator is also proposed following the ad-hoc procedure proposed by Gonzalez-Manteiga et al. (Comput Stat Data Anal 51:2720–2733, 2007). We then compare the performance of the proposed benchmarked estimator with several competing estimators through a set of simulation studies.