Cynthia Cooper 
_{Oregon State University
Department of Statistics
44 Kidder Hall
Corvallis OR 97330
Ph. 541-737-5936
E-mail:  cooper@stat.orst.edu}

Abstract
Model -based and design-based approaches to estimation differ in how variance of an estimator is quantified.  Design-based variance estimators account for covariance by incorporating within-cluster variance as used in multi -stage sampling.  The estimators are unbiased, intuitive and free of model assumptions, but require subsamples at all levels of the sample design  – a  problem in some stratified and systematic samples.  This potential inadequacy of data is analogous to small-area estimation scenarios.  Model -based quantification of mean square error, which combines variance of the underlying process and squared bias, will  not necessarily be representative of variation due to the sampling process.  In this paper, application of a model -assisted approach to quantifying variance due to the sampling process is explored.  The concept of employing a model of covariance is illustrated for two scenarios  – a model -based scenario in which the objective is to quantify precision of an estimate afforded by the sampling process; and a design-based scenario in which inadequate subsampling precludes quantifying within-cluster variance by direct estimation.  Application of a parametric model to quantify variance due to sampling is demonstrated to be more representative of the empirical variance observed in simulations of repeated samples on a fixed realization of a random process.  

Keywords:   model -based, design-based sampling/estimation, model -assisted variance estimation, kriging variance, continuous domain sampling, spatial covariance, non-exchangeable response

In: McRoberts, R. et al. (eds).  Proceedings of the joint meeting of The 6th International Symposium On Spatial Accuracy Assessment In Natural Resources and Environmental Sciences and The 15th Annual Conference of The International Environmetrics Society, June 28 – July 1 2004, Portland, Maine, USA.