Design-Based Predictive Inference

Design-based inference from probability samples is valid by construction for target parameters that are descriptive summaries of finite populations. We develop a novel approach of design-based predictive inference for finite populations, where the individual-level predictor is learned from a probability sample using any models or algorithms for incorporating the relevant auxiliary information, and the uncertainty of estimation is evaluated with respect to the known probability design while the outcome and auxiliary values for modeling are treated as constants. Unlike the existing theory of design-based model-assisted estimation for finite populations, design-based predictive inference is as well suited for individual-level prediction in addition to producing population-level estimates.