On the two-phase framework for joint model and design-based inference

• 成果类型: Article
• 署名作者: Rubin-Bleuer, S; Kratina, IS
• 署名单位: Statistics Canada
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000651
• 发表日期: 2005
• 页码: 2789-2810
• 关键词: varying probabilities; ASYMPTOTIC THEORY; variance-estimation; finite population; superpopulation; replacement; parameters; estimators; jackknife

摘要

We establish a mathematical framework that formally validates the twophase super-population viewpoint proposed by Hartley and Sielken [Biometrics 31 (1975) 411-422] by defining a product probability space which includes both the design space and the model space. The methodology we develop combines finite population sampling theory and the classical theory of infinite population sampling to account for the underlying processes that produce the data under a unified approach. Our key results are the following: first, if the sample estimators converge in the design law and the model statistics converge in the model, then, under certain conditions, they are asymptotically independent, and they converge jointly in the product space; second, the sample estimating equation estimator is asymptotically normal around a super-population parameter.