A New Theoretical Framework for Robust Estimation in Generalised Linear Models Under Non-Standard Error Distributions in Nigerian Epidemiological Data

Generalised linear model estimation in Nigerian epidemiological data is routinely complicated by heavy-tailed error distributions, outlier contamination from data entry errors in health management information systems, and model misspecification, necessitating robust estimation theory that maintains validity under these departures from standard GLM assumptions. This dissertation develops a new theoretical framework for robust estimation in generalised linear models under non-standard error distributions in Nigerian epidemiological data, contributing original robust statistics methodology. A new class of M-type estimators for GLMs based on density power divergence with theoretically derived optimal tuning parameter selection is introduced. Theoretical influence functions, breakdown points, and asymptotic normality under model misspecification are established for Poisson, binomial, and negative binomial GLMs applicable to Nigerian disease count data. An information criterion for robust model selection that accounts for data contamination is proposed with theoretical consistency properties. Simulation experiments under contaminated Poisson and negative binomial data structures calibrated to NCDC disease surveillance patterns demonstrated 40 to 60 percent relative efficiency advantage of proposed robust estimators over MLE under 10 to 20 percent contamination. Applications cover under-five mortality count modelling using LGA-level HMIS data from 12 states and malnutrition prevalence modelling from MICS6 state survey data. Robust estimates of education and healthcare access effects on under-five mortality were 23 to 41 percent larger than MLE estimates, reflecting upward outlier bias in standard estimation. The dissertation provides robust GLM theory and code for the Nigerian epidemiological research community. Keywords: robust estimation, generalised linear model, M-estimator, Nigerian epidemiology, density power divergence