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Optimal sampling and estimation strategies under linear model

Auteur(s)
Nedyalkova, Desislava 
Institut de statistique 
Tillé, Yves 
Institut de statistique 
Date de parution
2008-3-23
In
Biometrika
Vol.
3
No
95
De la page
521
A la page
537
Mots-clés
  • Balanced sampling Design-based inference Finite population sampling Fully explainable heteroscedasticity Model-assisted inference Model-based inference Optimal strategy
  • Balanced sampling Des...

Résumé
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.
Identifiants
https://libra.unine.ch/handle/123456789/14377
Type de publication
journal article
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