Sampling and variance estimation on continuous domains

摘要

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.