Scalable generalized accuracy estimation for multisource register-based official statistics

Official statistics are undergoing a significant transformation, as national statistical institutes transition from traditional single-source data production systems to integrated systems of statistical registers combining administrative, census, and survey data. The resulting multisource register-based estimates are prone to multiple interacting sources of error, yet rigorous scalable frameworks for quantifying their accuracy remain underdeveloped. This work discusses and validates a global measure of error assessment for such multisource register-based statistics. Focusing on two central sources of uncertainty-sampling and modelling-we derive an analytical solution that accurately approximates the global error of mass-imputation procedures under a multinomial logistic model. The proposed measure is interpretable, flexible, and computationally scalable, enabling on-the-fly accuracy quantification for user-defined, unplanned domain-specific statistics on population totals. Its validity is established theoretically and confirmed through simulation studies. An application to education data from the Italian National Institute of Statistics is presented.