Estimation of multi-way tables subject to coherence constraints
DOI:
https://doi.org/10.6092/issn.1973-2201/6348Keywords:
Population Census, Multi-way tables, Generalised Raking, Bayesian hierarchical modelsAbstract
Nowadays, traditional population censuses based on total enumeration of the population are being accompanied by sample surveys. Sampling within censuses allows to reduce costs and workload of authorities involved in censuses operations, along with the statistical burden for the people involved in the enumeration. In this paper, we deal with estimation of multi-way contingency tables involving variables measured both via census and sampling. In this framework, two main issues need to be addressed: first of all, sample size for estimating some of the entries of the contingency tables may be too small, delivering estimates prone to huge sampling variability. On the other hand, since estimates of the joint distribution need to be coherent with the marginal distribution of the variable collected via a census, estimation methods need to be coherent with the constraint imposed by marginal distribution of variables measured via census. The problem is tackled via a model-based approach that allows to comply with all coherence constraints following a fairly simple procedure. The merit of the proposed methodology is illustrated by means of a simulation study.References
O. BLUM (1999). Combining Register-Based and Traditional Census Processes as a Pre-Defined Strategy in Census Planning. Annual Conference of the Federal Committee on Statistical Methodology, Washington DC, USA.
B. CARPENTER, A. GELMAN, M. HOFFMAN, D. LEE, B. GOODRICH, M. BE TANCOURT, M. BRUBAKER, J. GUO, P. LI, A. RIDDELL (2016). Stan: A probabilistic programming language. Journal of Statistical Software, , no. In Press.
J. DEVILLE, C. SARNDAL, O. SAUTORY (1993). Generalized raking procedures in survey sampling. Journal of the American Statistical Association, 88, no. 423, pp. 1013–1020.
R. FAY, R. HERRIOT (1979). Estimates of income for small places: An application of james-stein procedures to census data. Journal of the American Statistical Association, 74, no. 366a, pp. 269–277.
L. GUNN, D. DUNSON (2005). A transformation approach for incorporating monotone or unimodal constraints. Biostatistics, 6, pp. 434–49.
ISTAT (2010). Beyond the 2010 census round: plans for the 2020 round. Economic Commission for Europe, Conference of European Statisticians, Geneva, 7-9 July 2010.
ISTAT (2012). A new strategy for the 2011 Lessons learned from use of registers and geocoded databases in population and housing census. Economic Commission for Europe, Conference of European Statisticians, Paris, 6-8 June 2012.
L. KISH (1979). Samples and censuses. International Statistical Review / Revue Internationale de Statistique, 47, no. 2, pp. 99–109.
R. LITTLE, M. WU (1991). Models for contingency tables with known margins when target and sampled populations differ. Journal of the American Statistical Association, 86, pp. 87–95.
D. LUNN, A. THOMAS, N. BEST, D. SPIEGELHALTER (2000). Winbugs – a bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, , no. 10, pp. 325–337.
E. MELILIL, G. PETRIS (1995). Bayesian inference for contingency tables with given marginals. Journal of the Italian Statistical Society, 2, pp. 215–233.
D. PFEFFERMANN, R. TILLER (2006). Small-area estimation with state: Space models subject to benchmark constraints. Journal of the American Statistical Association, 101, pp. 1387–1397.
J. RAO, I. MOLINA (2015). Small area estimation. 2nd Edition. John Wiley & Sons, Hoboken (N.J.).
R. C. STEORTS, M. GHOSH (2013). On estimation of mean squared errors of benchmarked empirical bayes estimators. Statistica Sinica, 23, no. 2, pp. 749–767.
UNECE (2007). Register-based statistics in the Nordic countries. United Nations, Geneva.
T. WRIGHT (1998). Sampling and censuses 2000: The concepts. American Scientist, 86, pp. 99–109.
Y. YOU, J. RAO, M. HIDIROGLOU (2013). On estimation of mean squared errors of benchmarked empirical bayes estimators. Survey Methodology, 39, no. 1, pp. 217–230.
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