Optimal sampling and estimation strategies under the linear model

• 成果类型: Article
• 署名作者: Nedyalkova, Desislava; Tille, Yves
• 署名单位: University of Neuchatel
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asn027
• 发表日期: 2008
• 页码: 521537
• 关键词: prediction; DESIGN

摘要

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.