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Nedyalkova, Desislava

Nom
Nedyalkova, Desislava
Affiliation principale
Identifiants
https://libra.unine.ch/handle/123456789/545

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  • Publication
    Métadonnées seulement
    Bias Robustness and Efficiency in Model-Based Inference
    (2012-9-4)
    Nedyalkova, Desislava 
    ;
    Tillé, Yves 
    In model-based inference, the selection of balanced samples has been considered to give protection against misspecification of the model. A recent development in finite population sampling is that balanced samples can be randomly selected. There are several possible strategies that use balanced samples. We give a definition of balanced sample that embodies overbalanced, mean-balanced, and $\pi$-balanced samples, and we derive strategies in order to equalize a $d$-weighted estimator with the best linear unbiased estimator. We show the value of selecting a balanced sample with inclusion probabilities proportional to the standard deviations of the errors with the Horvitz-Thompson estimator. This is a strategy that is design-robust and efficient. We show its superiority compared to other strategies that use balanced samples in the model-based framework. In particular, we show that this strategy is preferable to the use of overbalanced samples in the polynomial model. The problem of bias-robustness is also discussed, and we show how overspecifying the model can protect against misspecification.
  • Publication
    Accès libre
    Optimal sampling and estimation strategies under the linear model
    Nedyalkova, Desislava 
    ;
    Tillé, Yves 
    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.