Estimation of contingency tables in complex survey sampling using probabilistic expert systems |
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Authors: | Marco Ballin Mauro Scanu Paola Vicard |
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Institution: | 1. ISTAT (DPTS-DCSP), via Adolfo Ravà 150, 00142 Roma, Italy;2. ISTAT (DPTS-DCET), via Cesare Balbo 16, 00184 Roma, Italy;3. Dipartimento di Economia, Università Roma Tre, via Silvio D’Amico 77, 00145 Roma, Italy |
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Abstract: | In this paper we explore the possibility to use a particular class of models, known as probabilistic expert systems, to define two classes of estimators of a contingency table in case of stratified sampling designs. The two classes are characterized by the different role of the sampling design: in the first, the sampling design is treated as an additional variable; in the second, it is used only for estimation purposes by means of the survey weights. The bias/variance trade off of these estimators is analyzed and the consequences of model misspecification are illustrated. Furthermore, it is shown that the Horvitz–Thompson estimator belongs to both classes of estimators. It comes out that the Horvitz–Thompson estimator is almost always inefficient but robust. Monte Carlo simulations illustrate the efficiency of the proposed estimators. |
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Keywords: | Bayesian networks Chain rule Stratified sampling design Structural learning |
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