Original Contributions to the Theory of High-Dimensional Regression with Sparse Structure for Genomic Data Applications in Nigerian Population Health Research

High-dimensional genomic data, where the number of predictors vastly exceeds sample size, is increasingly generated in Nigerian population health research but analysed using methods developed for European ancestry populations that may not preserve valid statistical inference under African linkage disequilibrium and haplotype structures. This dissertation makes original theoretical contributions to high-dimensional sparse regression methods applicable to Nigerian genomic population health data. New theoretical guarantees for LASSO, adaptive LASSO, and SCAD estimators are derived under design matrix conditions typical of West African SNP data: high correlation structure, population stratification, and admixed ancestry. A novel African ancestry-adaptive penalised regression estimator (AAPR) is introduced with theoretical consistency and oracle property proofs under relaxed conditions compared to existing methods. Simulation experiments calibrated to Yoruba and Hausa ancestry LD structures from the 1000 Genomes Project demonstrated that AAPR achieved 18 percent lower false discovery rate and 24 percent higher power for true signal identification than standard LASSO. The AAPR method was applied to identify SNP predictors of hypertension in 1,200 Yoruba participants from the University College Hospital Ibadan cardiovascular genetics study. Seventeen novel loci passed FDR correction, including three with no prior European ancestry associations. The dissertation contributes methodological theory with direct application to expanding Nigerian genomic epidemiology research infrastructure. Keywords: high-dimensional regression, LASSO, sparse estimation, genomic data, Nigerian population health