Formal Statistical Theory for Multi-Source Data Fusion Under Uncertainty in the Context of Nigeria’s National Statistical System Modernisation

Nigeria's National Statistical System is modernising to incorporate satellite imagery, mobile phone data, and administrative records alongside traditional surveys, but a formal statistical theory for fusing these heterogeneous data sources under differential quality, coverage, and timeliness does not yet exist for the Nigerian context. This dissertation develops formal statistical theory for multi-source data fusion under uncertainty applicable to Nigeria's National Statistical System (NSS) modernisation agenda. A decision-theoretic framework for optimal data source combination is developed, minimising weighted mean squared error across fused estimates under source-specific reliability characterised by coverage probability, measurement bias, and temporal lag parameters. New identifiability conditions for fused estimators when source biases are unknown are derived, and a bias-correction procedure using anchor survey sub-samples is theoretically justified. Asymptotic theory for fused estimators under unknown source error structure is established using empirical process methods. Applications develop fusion estimators for three NSS priority indicators: LGA-level poverty rate fusing NLSS survey, NHIA claims, and Landsat land use data; quarterly GDP growth fusing national accounts, satellite nighttime light, and CBN credit growth data; and LGA child immunisation rate fusing MICS survey, NPHCDA DHIS2, and mobile phone mobility data. Fused GDP growth forecasts achieved RMSE improvement of 31 percent over survey-only nowcasts. Poverty rate fusion reduced mean LGA estimation error by 44 percent. The dissertation provides NBS with theoretically grounded data fusion methodology for the Nigeria Statistical Master Plan 2025 to 2030 implementation. Keywords: data fusion, multi-source integration, Nigeria statistical system, decision-theoretic estimation, official statistics