Developing a Theoretical Foundation for Adaptive Survey Designs in Low-Resource Settings: Applications to Agricultural Census Methodology in Nigeria

Adaptive survey designs that modify data collection procedures in response to accumulated sample information offer theoretical efficiency advantages in low-resource settings where traditional fixed designs are too costly to achieve target precision, yet their theoretical foundations for agricultural census applications in Nigeria have not been established. This dissertation develops theoretical foundations for adaptive survey designs applicable to agricultural census methodology in Nigeria, contributing original design-based and model-assisted estimation theory. New theoretical results on unbiasedness and variance estimation for adaptive cluster sampling and two-phase adaptive designs are derived for non-standard population structures reflecting Nigerian smallholder farm spatial distributions. Optimal adaptation rules under cost constraints are derived using Lagrangian optimisation, yielding theoretical efficiency bounds relative to comparable fixed-cost designs. Simulation experiments calibrated to data from the 2019 General Household Survey Panel confirmed 31 percent variance reduction for small farm area estimation using proposed adaptive designs compared to standard stratified sampling at equal cost. The theory was implemented in a pilot adaptive census of smallholder farms in three Kogi State LGAs, with adaptation based on observed farm size clustering. Design-based variance estimates from the pilot showed 27 percent efficiency improvement over NBS fixed-design benchmarks for small-farm count estimation. The dissertation provides the National Population Commission and NBS with a theoretically grounded adaptive design framework for the next Nigerian Agricultural Census, with implementation guidelines and open-source R code. Keywords: adaptive survey design, agricultural census, Nigeria, design-based estimation, sampling theory