Sampling and variance estimation on continuous domains

This paper explores fundamental concepts of design‐ and model‐based approaches to sampling and estimation for a response defined on a continuous domain. The paper discusses the concepts in design‐based methods as applied in a continuous domain, the meaning of model‐based sampling, and the interpretation of the design‐based variance of a model‐based estimate. A model‐assisted variance estimator is examined for circumstances for which a direct design‐based estimator may be inadequate or not available. The alternative model‐assisted variance estimator is demonstrated in simulations on a realization of a response generated by a process with exponential covariance structure. The empirical results demonstrate that the model‐assisted variance estimator is less biased and more efficient than Horvitz–Thompson and Yates–Grundy variance estimators applied to a continuous‐domain response. Copyright © 2006 John Wiley & Sons, Ltd.