Penalized Calibration in Survey Sampling: Design-Based Estimation Assisted by Mixed Models

Fabien Guggemos & Yves Tillé

Abstract Calibration techniques in survey sampling, such as generalized regression estimation (GREG), were formalized in the 1990s to produce efficient estimators of linear combinations of study variables, such as totals or means. They implicitly lie on the assumption of a linear regression model between the variable of interest and some auxiliary variables in order to yield estimates with lower variance if the model is true and remaining approximately design-unbiased even if the model does not hold. We propose a new class of model-assisted estimators obtained by releasing a few calibration constraints and replacing them with a penalty term. This penalization is added to the distance criterion to minimize. By introducing the concept of penalizedcalibration, combining usual calibration and this ‘relaxed’ calibration, we are able to adjust the weight given to the available auxiliary information. We obtain a more flexible estimation procedure giving better estimates particularly when the auxiliary information is overly abundant or not fully appropriate to be completely used. Such an approach can also be seen as a design-based alternative to the estimation procedures based on the more general class of mixedmodels, presenting new prospects in some scopes of application such as inference on small domains.
Citation Guggemos, F., & Tillé, Y. (2010). Penalized Calibration in Survey Sampling: Design-Based Estimation Assisted by Mixed Models. Journal of Statistical Planning and Inference, 140(11), 3199-3212.
Type Journal article (English)
Date of appearance 23-3-2010
Journal Journal of Statistical Planning and Inference
Volume 140
Issue 11
Pages 3199-3212
URL http://www.sciencedirect.com/science/article/pii/S0378375...
Related project Convention Université de Neuchâtel/Office fédéral de la s...