Smoothed model-assisted small area estimation of proportions

In countries where population census data are limited, generating accurate subnational estimates of health and demographic indicators is challenging. Existing model-based geostatistical methods leverage covariate information and spatial smoothing to reduce the variability of estimates but often ignore the survey design, while traditional small area estimation approaches may not incorporate both unit-level covariate information and spatial smoothing in a design consistent way. We propose a smoothed model-assisted estimator that accounts for survey design and leverages both unit-level covariates and spatial smoothing. Under certain regularity assumptions, this estimator is both design consistent and model consistent. We compare it with existing design-based and model-based estimators using real and simulated data.