Fully Bayesian Benchmarking of Small Area Estimation Models

Albert, I., S. Donnet, C. Guihenneuc-Jouyaux, S. Low-Choy, K. Mengersen, and J. Rousseau. 2012. “Combining expert opinions in prior elicitation.” Bayesian Analysis 7(3): 503–532. DOI: https://doi.org/10.1214/12-BA717.10.1214/12-BA717Search in Google Scholar

Bell, W.R., G.S. Datta, and M. Ghosh. 2013. “Benchmarking small area estimators.” Biometrika 100(1): 189–202. DOI: https://doi.org/10.1093/biomet/ass063.10.1093/biomet/ass063Search in Google Scholar

Berg, E. and W. Fuller. 2009. “A SPREE Small Area Procedure for Estimating Population Counts”. In Proceedings of the Survey Methods Section, Statistical Society of Canada. Section on Survey Methods, Statistical Society of Canada. Available at: http://www.ssc.ca/survey/documents/SSC2009_EBerg.pdf (accessed August 2019).Search in Google Scholar

Berg, E.J., W.A. Fuller, and A.L. Erciulescu. 2012. “Benchmarked small area prediction.” In Proceedings of the Section on Research Methods, Joint Statistical Meeting. Section on Research Methods, Joint Statistical Meeting. Available at: http://www.asasrms.org/Proceedings/y2012/Files/305110_74288.pdf (accessed August 2019).Search in Google Scholar

Datta, G.S., M. Ghosh, R. Steorts, and J. Maples. 2011. “Bayesian benchmarking with applications to small area estimation.” TEST 20(3): 574–588. DOI: https://doi.org/10.1007/s11749-010-0218-y.10.1007/s11749-010-0218-ySearch in Google Scholar

De Waal, T. 2016. “Obtaining numerically consistent estimates from a mix of administrative data and surveys.” Statistical Journal of the IAOS 32(2): 231–243. DOI: https://doi.org/10.3233/SJI-150950.10.3233/SJI-150950Search in Google Scholar

Elbers, C., J.O. Lanjouw, and P. Lanjouw. 2003. “Micro-level estimation of poverty and inequality.” Econometrica 71(1): 355–364. DOI: https://doi.org/10.1111/1468-0262.00399.10.1111/1468-0262.00399Search in Google Scholar

Fabrizi, E., C. Giusti, N. Salvati, and N. Tzavidis. 2014. “Mapping average equivalized income using robust small area methods.” Papers in Regional Science 93: 685–701. DOI: https://doi.org/10.1111/pirs.12015.10.1111/pirs.12015Search in Google Scholar

Fabrizi, E., N. Salvati, and M. Pratesi. 2012. “Constrained small area estimators based on M-quantile methods.” Journal of Official Statistics 28(1): 89–106. Available at: https://www.scb.se/contentassets/ff271eeeca694f47ae99b942de61df83/constrained-small-area-estimators-based-on-m-quantile-methods.pdf (accessed August 2019).Search in Google Scholar

Fay, R.E. and R.A. Herriot. 1979. “Estimates of income from small places: an application of James-Stein procedures to census data.” Journal of the American Statistical Association 74: 269–277. DOI: https://doi.org/10.1080/01621459.1979.10482505.10.1080/01621459.1979.10482505Search in Google Scholar

Gelman, A., J. Carlin, H. Stern, D. Dunson, A. Vehtari, and D. Rubin. 2014. Bayesian Data Analysis, Third Edition. New York: Chapman and Hall.10.1201/b16018Search in Google Scholar

Gelman, A., A. Jakulin, M.G. Pittau, and Y.-S. Su. 2008. “A weakly informative default prior distribution for logistic and other regression models.” The Annals of Applied Statistics 2: 1360–1383. DOI: https://doi.org/10.1214/08-AOAS191.10.1214/08-AOAS191Search in Google Scholar

Ghosh, M., T. Kubokawa, and Y. Kawakubo. 2015. “Benchmarked empirical Bayes methods in multiplicative area-level models with risk evaluation.” Biometrika 102(3): 647–659. DOI: https://doi.org/10.1093/biomet/asv010.10.1093/biomet/asv010Search in Google Scholar

Lindley, D.V. 1983. “Reconciliation of Probability Distributions.” Operations Research 31: 866–880. DOI: https://doi.org/10.1287/opre.31.5.866.10.1287/opre.31.5.866Search in Google Scholar

Lindley, D.V., A. Tversky, and R.V. Brown. 1979. “On the Reconciliation of Probability Assessments (with discussion).” Journal of the Royal Statistical Society, Series A 142: 146–180. DOI: https://doi.org/10.2307/2345078.10.2307/2345078Search in Google Scholar

Little, R.J. 2012. “Calibrated Bayes, an alternative inferential paradigm for official statistics.” Journal of Official Statistics 28(3): 309. Available at: https://www.scb.se/contentassets/ca21efb41fee47d293bbee5bf7be7fb3/calibrated-bayes-an-alternative-inferential-paradigm-for-official-statistics.pdf (accessed August 2019).Search in Google Scholar

Lumley, T. 2004. “Analysis of Complex Survey Samples.” Journal of Statistical Software 9(1): 1–19. DOI: https://doi.org/10.18637/jss.v009.i08.10.18637/jss.v009.i08Search in Google Scholar

Lumley, T. 2011. Complex surveys: A guide to analysis using R, Volume 565. John Wiley & Sons.10.1002/9780470580066Search in Google Scholar

Morris, P.A. 1974. “Decision Analysis Expert Use.” Management Science 20: 1233–1241. DOI: https://doi.org/10.1287/mnsc.20.9.1233.10.1287/mnsc.20.9.1233Search in Google Scholar

Morris, P.A. 1977. “Combining Expert Judgements: A Bayesian Approach.” Management Science 23: 679–693. DOI: https://doi.org/10.1287/mnsc.23.7.679.10.1287/mnsc.23.7.679Search in Google Scholar

Nandram, B. and H. Sayit. 2011. “A Bayesian analysis of small area probabilities under a constraint.” Survey Methodology 37: 137–152. Available at: www.150.statcan.gc.ca/n1/pub/12-001-x/2011002/article/11603-eng.pdf (accessed August 2019).Search in Google Scholar

Nandram, B., M.C.S. Toto, and J.W. Choi. 2011. “A Bayesian benchmarking of the Scott- Smith model for small areas.” Journal of Statistical Computation and Simulation 81(11): 1593–1608. DOI: https://doi.org/10.1080/00949655.2010.496726.10.1080/00949655.2010.496726Search in Google Scholar

O’Hagan, A., C.E. Buck, A. Daneshkhah, J.R. Eiser, P.H. Garthwaite, D.J. Jenkenson, J.E. Oakley, and T. Rakow. 2006. Eliciting Experts’ Probabilities. John Wiley and Sons, Ltd.Search in Google Scholar

Pfeffermann, D. 2013. “New important developments in small area estimation.” Statistical Science 28(1): 40–68. DOI: https://doi.org/10.1214/12-STS395.10.1214/12-STS395Search in Google Scholar

Pfeffermann, D. and C.H. Barnard. 1991. “Some new estimators for small-area means with application to the assessment of farmland values.” Journal of Business & Economic Statistics 9(1): 73–84. DOI: https://doi.org/10.1080/07350015.1991.10509828.10.1080/07350015.1991.10509828Search in Google Scholar

Pfeffermann, D., A. Sikov, and R. Tiller. 2014. “Single-and two-stage cross-sectional and time series benchmarking procedures for small area estimation.” TEST 23(4): 631–666. DOI: https://doi.org/10.1007/s11749-014-0400-8.10.1007/s11749-014-0400-8Search in Google Scholar

Pfeffermann, D. and R. Tiller. 2006. “Small-area estimation with state-space models subject to benchmark constraints.” Journal of the American Statistical Association 101(476): 1387–1397. DOI: https://doi.org/10.1198/016214506000000591.10.1198/016214506000000591Search in Google Scholar

Poole, D. and A.E. Raftery. 2000. “Inference for deterministic simulation models: The Bayesian melding approach.” Journal of the American Statistical Association 95: 1244–1255. DOI: https://doi.org/10.1080/01621459.2000.10474324.10.1080/01621459.2000.10474324Search in Google Scholar

Prado, R. and M. West. 2010. Time series: modeling, computation, and inference. CRC Press.10.1201/9781439882757Search in Google Scholar

Preston, S., P. Heuveline, and M. Guillot. 2001. Demography: Modelling and Measuring Population Processes. Oxford: Blackwell.Search in Google Scholar

Ranalli, M.G., G.E. Montanari, and C. Vicarelli. 2018. “Estimation of small area counts with the benchmarking property.” Metron 76(3): 349–378. DOI: https://doi.org/10.1007/s40300-018-0146-2.10.1007/s40300-018-0146-2Search in Google Scholar

Rao, J.N.K. and I. Molina. 2015. Small area estimation, Second edition. John Wiley & Sons.10.1002/9781118735855Search in Google Scholar

Roback, P.J. and G.H. Givens. 2001. “Supra-Bayesian pooling of priors linked by a deterministic simulation model.” Communications in Statistics-Simulation and Computation 30(3): 447–476. DOI: https://doi.org/10.1081/SAC-100105073.10.1081/SAC-100105073Search in Google Scholar

Steorts, R.C. and M. Ghosh. 2013. “On estimation of mean squared errors of benchmarked empirical Bayes estimators.” Statistica Sinica 23(2): 749–767. DOI: https://doi.org/10.5705/ss.2012.053.10.5705/ss.2012.053Search in Google Scholar

Toto, M.C.S. and B. Nandram. 2010. “A Bayesian predictive inference for small area means incorporating covariates and sampling weights.” Journal of Statistical Planning and Inference 140(11): 2963–2979. DOI: https://doi.org/10.1016/j.jspi.2010.03.043.10.1016/j.jspi.2010.03.043Search in Google Scholar

U.S. Census Bureau. 2014. “Model-based Small Area Income and Poverty Estimates (SAIPE) for School Districts, Counties, and States” (accessed July 2014).Search in Google Scholar

Vesper, A.J. 2013. Three Essays of Applied Bayesian Modeling: Financial Return Contagion, Benchmarking Small Area Estimates, and Time-Varying Dependence. PhD thesis, Harvard University. Available at: https://dash.harvard.edu/handle/1/11124829 (accessed August 2019).Search in Google Scholar

Wang, J., W.A. Fuller, and Y. Qu. 2008. “Small area estimation under a restriction.” Survey Methodology 34(1): 29. Available at: www150.statcan.gc.ca/n1/pub/12-001-x/2008001/article/10619-eng.pdf (accessed August 2019).Search in Google Scholar

You, Y. and J. Rao. 2002. “A pseudo-empirical best linear unbiased prediction approach to small area estimation using survey weights.” Canadian Journal of Statistics 30(3): 431–439. DOI: https://doi.org/10.2307/3316146.10.2307/3316146Search in Google Scholar

You, Y. and J. Rao. 2003. “Pseudo hierarchical Bayes small area estimation combining unit level models and survey weights.” Journal of Statistical Planning and Inference 111: 197–208. DOI: https://doi.org/10.1016/S0378-3758(02)00301-4.10.1016/S0378-3758(02)00301-4Search in Google Scholar

You, Y., J. Rao, and P. Dick. 2004. “Benchmarking hierarchical Bayes small area estimators in the Canadian census undercoverage estimation.” Statistics in Transition 6: 631–640. Available at: https://pts.stat.gov.pl/en/journals/statistics-in-transition/ (accessed February 2020).Search in Google Scholar

You, Y., J. Rao, and M. Hidiroglou. 2013. “On the performance of self benchmarked small area estimators under the Fay-Herriot area level model.” Survey Methodology 39: 217–230. Available at: www150.statcan.gc.ca/n1/pub/12-001-x/2013001/article/11830-eng.htm (accessed August 2019).Search in Google Scholar