If the heteroscedasticity of the model is fully explainable by the auxiliary variables, then this strategy is also optimal in a model-based sense. We show that, under a linear model, the optimal model-assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the Horvitz Thompson estimator. These two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator, a strategy being a pair composed of a sampling design and an estimator. 1 Biometria (008), 95, 3,pp C 008 Biometria Trust Printed in Great Britain doi: /biomet/asn07 Optimal sampling and estimation strategies under the linear model BY DESISLAVA NEDYALKOVA AND YVES TILLÉ Institute of Statistics, University of Neuchâtel, Pierre à Mazel 7, 000 Neuchâtel, Switzerland SUMMARY In some cases model-based and model-assisted inferences can lead to very different estimators.
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