Smoothed Model-Assisted Small Area Estimation

In countries where population census and sample survey 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 assume the survey design is ignorable, which may be inappropriate given the complex design of household surveys typically used in this context. On the other hand, small area estimation approaches common in the survey statistics literature do not incorporate both unit-level covariate information and spatial smoothing in a design-consistent way. We propose a new smoothed model-assisted estimator that accounts for survey design and leverages both unit-level covariates and spatial smoothing, bridging the survey statistics and model-based geostatistics perspectives. Under certain assumptions, the new estimator can be viewed as both design-consistent and model-consistent, offering potential benefits from both perspectives. We demonstrate our estimator's performance using both real and simulated data, comparing it with existing design-based and model-based estimators.