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Bias Robustness and Efficiency in Model-Based Inference
Abstract 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.
   
Keywords Balanced sampling, finite population sampling, polynomial model, ratio model, robust estimation
   
Citation Nedyalkova, D., & Tillé, Y. (2012). Bias Robustness and Efficiency in Model-Based Inference. Statistica Sinica, 22, 777-794.
   
Type Journal article (English)
Date of appearance 4-9-2012
Journal Statistica Sinica
Volume 22
Pages 777-794
URL http://www3.stat.sinica.edu.tw/statistica/oldpdf/A22n215.pdf
Related project Convention Université de Neuchâtel/Office fédéral de la s...