Advancements in statistical methodology, theory, and algorithms for combining multiple data sources

Abstract

This dissertation develops novel statistical methodology, theoretical foundations, and computational algorithms for granular estimation in finite populations by integrating multiple data sources. Motivated by the growing availability of heterogeneous data, ranging from traditional probability surveys to modern nonprobability samples, this work addresses key challenges in producing reliable subgroup level estimates when direct observations are sparse or unavailable. Chapter 2 develops theoretical foundations for interval estimation in small area models, proposing probability matching priors that reconcile empirical Bayes and hierarchical Bayes approaches and achieve second-order accurate coverage. Chapter 3 introduces a model-based data integration framework for combining multiple probability surveys using generalized linear mixed models, along with Expectation Maximization based estimation and parametric bootstrap methods for uncertainty quantification. Chapter 4 extends data integration framework to integrate probability and nonprobability surveys, proposing a composite estimator that addresses selection bias and measurement error simultaneously, with machine learning methods incorporated for bias correction in complex settings. Collectively, this work provides a unified framework for statistical data integration that improves estimation accuracy, uncertainty quantification, and methodological robustness in granular inference problems. The proposed methods have direct applications in official statistics and public policy, enabling more precise and reliable estimates for targeted decision-making across small geographic areas and demographic subpopulations.