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Optimal sampling and estimation strategies under the linear model

Nedyalkova, Desislava ; Tillé, Yves

In: Biometrika, 2008, vol. 95, no. 3, p. 521-537

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    Titel
    • Optimal sampling and estimation strategies under the linear model
    Autor
    • Nedyalkova, Desislava. University of Neuchâtel, Institute of Statistics, Pierre à Mazel 7, 2000 Neuchâtel, Switzerland
    • Tillé, Yves. University of Neuchâtel, Institute of Statistics, Pierre à Mazel 7, 2000 Neuchâtel, Switzerland
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Biometrika, 2008, vol. 95, no. 3, p. 521-537. Oxford University Press
    Andere elektronische Ausgabe
    OAI-PMH-ID
    • oai:doc.rero.ch:298834
    Summary
    In some cases model-based and model-assisted inferences can lead to very different estimators. 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. 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. If the heteroscedasticity of the model is ‚fully explainable' by the auxiliary variables, then this strategy is also optimal in a model-based sense. Moreover, under balanced sampling and with inclusion probabilities that are proportional to the standard deviation of the model, the best linear unbiased estimator and the Horvitz-Thompson estimator are equal. Finally, it is possible to construct a single estimator for both the design and model variance. The inference can thus be valid under the sampling design and under the model