Randomization-assisted model-based survey sampling

The model-assisted paradigm presently dominates survey sampling. Under it, randomization-based theory is treated as the only true approach to inference. Models are helpful only when choosing between randomization-based methods. We propose an alternative theoretical paradigm. Model-based inference, which conditions on the realized sample, is the focus of this approach. Randomization-based methods, which focus on the set of hypothetical samples that could have been drawn, are employed primarily to provide protection against model failure. Although the choices made under the randomization-assisted model-based paradigm are often little different from those recommended by Särndal et al. (Model Assisted Survey Sampling, Springer, New York, 1992), the motivation is clearer. Moreover, the approach proposed here for variance estimation leads to a logically coherent treatment of finite-population and small-sample adjustments when they are needed.