  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
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 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.
