The sample of the Statistical survey on population by ethnicity, native language and religion 2021 consists of the voluntary sample and the probability sample drawn from the rest of the census population. A natural post-stratified calibrated estimator underestimates minor religions and other small proportions of interest. Alternatively, to correct the selection bias of estimates based on the non-probability sample, we fit a model for propensity scores using the demographic and socioeconomic data and information from the previous complete census. Then we combine the inverse probability weighted and doubly robust estimators with post-stratified calibrated estimators. The total sample size of the survey is not sufficient to derive accurate direct estimates of the proportions in small domains like municipalities. We apply robust design-based composite estimators which exploit domain-level information on the study variables from the previous census.
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