Have a personal or library account? Click to login
Fully Bayesian Benchmarking of Small Area Estimation Models Cover

Fully Bayesian Benchmarking of Small Area Estimation Models

By: Junni L. Zhang and  John Bryant  
Open Access
|Mar 2020

References

  1. 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-BA717
  2. 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/ass063
  3. 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).
  4. 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).
  5. 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-y
  6. 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-150950
  7. 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/10.1111/1468-0262.00399.10.1111/1468-0262.00399
  8. 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.12015
  9. 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).
  10. 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/10.1080/01621459.1979.10482505.10.1080/01621459.1979.10482505
  11. 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/b16018
  12. 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-AOAS191
  13. 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/asv010
  14. 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.31.5.866
  15. 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/10.2307/2345078.10.2307/2345078
  16. 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).
  17. 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.i08
  18. Lumley, T. 2011. Complex surveys: A guide to analysis using R, Volume 565. John Wiley & Sons.10.1002/9780470580066
  19. 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.20.9.1233
  20. 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.23.7.679
  21. 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).
  22. 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/10.1080/00949655.2010.496726.10.1080/00949655.2010.496726
  23. 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.
  24. 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-STS395
  25. 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/10.1080/07350015.1991.10509828.10.1080/07350015.1991.10509828
  26. 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/s11749-014-0400-8
  27. 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/10.1198/016214506000000591.10.1198/016214506000000591
  28. 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/10.1080/01621459.2000.10474324.10.1080/01621459.2000.10474324
  29. Prado, R. and M. West. 2010. Time series: modeling, computation, and inference. CRC Press.10.1201/9781439882757
  30. Preston, S., P. Heuveline, and M. Guillot. 2001. Demography: Modelling and Measuring Population Processes. Oxford: Blackwell.
  31. 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/s40300-018-0146-2
  32. Rao, J.N.K. and I. Molina. 2015. Small area estimation, Second edition. John Wiley & Sons.10.1002/9781118735855
  33. 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-100105073
  34. 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.2012.053
  35. 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.2010.03.043
  36. U.S. Census Bureau. 2014. “Model-based Small Area Income and Poverty Estimates (SAIPE) for School Districts, Counties, and States” (accessed July 2014).
  37. 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).
  38. 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).
  39. 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/10.2307/3316146.10.2307/3316146
  40. 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)00301-4
  41. 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).
  42. 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).
Language: English
Page range: 197 - 223
Submitted on: Nov 1, 2018
|
Accepted on: Sep 1, 2019
|
Published on: Mar 17, 2020
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2020 Junni L. Zhang, John Bryant, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.