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December 2005 On the two-phase framework for joint model and design-based inference
Susana Rubin-Bleuer, Ioana Schiopu Kratina
Ann. Statist. 33(6): 2789-2810 (December 2005). DOI: 10.1214/009053605000000651


We establish a mathematical framework that formally validates the two-phase “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.


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Susana Rubin-Bleuer. Ioana Schiopu Kratina. "On the two-phase framework for joint model and design-based inference." Ann. Statist. 33 (6) 2789 - 2810, December 2005.


Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1084.62020
MathSciNet: MR2253102
Digital Object Identifier: 10.1214/009053605000000651

Primary: 62F12
Secondary: 62D05

Keywords: Joint design and model-based inference

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 6 • December 2005
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