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Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model Cover

Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model

Open Access
|Mar 2016

References

  1. Ando, T. 2007. “Bayesian Predictive Information Criterion for the Evaluation of Hierarchical Bayesian and Empirical Bayes Models.” Biometrika 94: 443-458. Doi: http://dx.doi.org/10.1093/biomet/asm017.10.1093/biomet/asm017
  2. Bedrick, E.J. 1983. “Adjusted Chi-Squared Tests for Cross-Classified Tables of Survey Data.” Biometrika 70: 591-595. Doi: http://dx.doi.org/10.1093/biomet/70.3.591.10.1093/biomet/70.3.591
  3. Brier, S.S. 1980. “Analysis of Contingency Tables Under Cluster Sampling.” Biometrika 67: 591-596. Doi: http://dx.doi.org/10.1093/biomet/67.3.591.10.1093/biomet/67.3.591
  4. Calsyn, C., P. Gonzales, and M. Frase. 1999. “Highlights from TIMSS.” National Center for Education Statistics, Washington, DC. Doi: http://mces.ed.gov/timss.
  5. Datta, G.S. and M. Ghosh. 1991. “Bayesian Prediction in Linear Models: Applications to Small Area Estimation.” Annals of Statistics 19: 1748-1770.10.1214/aos/1176348369
  6. Foy, P., K. Rust, and A. Schleicher. 1996. “Sample Design.” In TIMMS Technical Report, Volume I: Design and Development, edited by M.O. Martin and D.L. Kelly, pagenumber. Chestnut Hill, MA: Boston College.
  7. Fuller, W.A. and G.E. Battese. 1973. “Transformations for Estimation of Linear Models with Nested-Error Structure.” Journal of the American Statistical Association 68: 626-632. Doi: http://dx.doi.org/10.1080/01621459.1973.10481396.10.1080/01621459.1973.10481396
  8. Gelfand, A., D. Dey, and H. Chang. 1992. “Model Determination using Predictive Distributions with Implementation via Sampling-based Methods.” In Bayesian Statistics 4, 147-168. New York: Oxford University Press.
  9. Geisser, S. and W. Eddy. 1979. “A Predictive Approach to Model Selection.” Journal of the American Statistical Association 74: 153-160. Doi: http://dx.doi.org/10.1080/01621459.1979.10481632.10.1080/01621459.1979.10481632
  10. Gelman, A., J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin. 2013. Bayesian Data Analysis, 3rd ed. New York: Chapman & Hall/CRC.10.1201/b16018
  11. Ghosh, M. and P. Lahiri. 1988. “Bayes and Empirical Bayes Analysis in Multistage Sampling.” In Statistical Decision Theory and Related Topics IV, Vol. 1, edited by S.S. Gupta and J.O. Berger. 195-212. New York: Springer.10.1007/978-1-4613-8768-8_22
  12. Hamilton, J. 2009. President Obama, U.S. Secretary of Education Duncan Announce National Competition to Advance School Reform. U.S. Department of Education: Available at: http://www.ed.gov/news/pressreleases/2009/07/07242009.html.
  13. Holt, D., A.J. Scott, and P.D. Ewings. 1980. “Chi-Squared Tests with Survey Data.” Journal of the Royal Statistical Society, Series A 143: 303-320. Doi: http://dx.doi.org/10.2307/2982131.10.2307/2982131
  14. Malec, D. and J. Sedransk. 1985. “Bayesian Inference for Finite Population Parameters in Multistage Cluster Sampling.” Journal of the American Statistical Association 80: 897-902. Doi: http://dx.doi.org/10.1080/01621459.1985.10478200.10.1080/01621459.1985.10478200
  15. Molina, I., B. Nandram, and J.N.K. Rao. 2014. “Small Area Estimation of General Parameters with Application to Poverty Indicators: A Hierarchical Bayes Approach.” Annals of Applied Statistics 8: 852-885. Doi: http://dx.doi.org/10.1214/13-AOAS702.10.1214/13-AOAS702
  16. Nandram, B. 2014. Bayesian Predictive Inference for a Proportion Under a Two-Fold Small Area Model. Technical Report, Department of Mathematical Sciences, Worcester Polytechnic Institute, 1-43. (Available on request.) Nandram, B., D.R. Bhatta, J. Sedransk, and D. Bhadra. 2013. “A Bayesian Test of Independence in a Two-Way Contingency Table Using Surrogate Sampling.” Journal of Statistical Planning and Inference 143: 1392-1408. Doi: http://dx.doi.org/10.1016/j.jspi.2013.03.011.10.1016/j.jspi.2013.03.011
  17. Nandram, B. 1998. “A Bayesian Analysis of the Three-Stage Hierarchical Multinomial Model.” Journal of Statistical Computation and Simulation 61: 97-126. Doi: http://dx.doi.org/10.1080/00949659808811904.10.1080/00949659808811904
  18. Nandram, B. and J. Sedransk. 1993. “Bayesian Predictive Inference for a Finite Population Proportion: Two-Stage Cluster Sampling.” Journal of the Royal Statistical Society, Series B 55: 399-408.10.1111/j.2517-6161.1993.tb01910.x
  19. Natarajan, R. and R.E. Kass. 2000. “Reference Bayesian Methods for Generalized Linear Mixed Models.” Journal of the American Statistical Association 95: 227-237. Doi: http://dx.doi.org/10.1080/01621459.2000.10473916.10.1080/01621459.2000.10473916
  20. Rao, J.N.K. 2003. Small Area Estimation. New York: Wiley.10.1002/0471722189
  21. Rao, J.N.K. and A.J. Scott. 1981. “The Analysis of Categorical Data from Complex Sample Surveys: Chi-squared Tests for Goodness of Fit and Independence in Two-Way Tables.” Journal of the American Statistical Association 76: 221-230. Doi: http://dx.doi.org/10.1080/01621459.1981.10477633.10.1080/01621459.1981.10477633
  22. Rao, J.N.K. and A.J. Scott. 1984. “On Chi-Squared Tests for Multi-way Tables with Cell Proportions Estimated from Survey Data.” Annals of Statistics 12: 46-60.10.1214/aos/1176346391
  23. Scott, A.J. and D. Holt. 1982. “The Effect of Two-Stage Sampling on Ordinary Least Squares Methods.” Journal of the American Statistical Association 77: 848-854. Doi: http://dx.doi.org/10.1080/01621459.1982.10477897.10.1080/01621459.1982.10477897
  24. Scott, A. and T.M.F. Smith. 1969. “Estimation in Multi-Stage Surveys.” Journal of the American Statistical Association 101: 1387-1397. Doi: http://dx.doi.org/10.1080/01621459.1969.10501015.10.1080/01621459.1969.10501015
  25. Silverman, B.W. 1986. Density Estimation for Statistics and Data Analysis. New York: Chapman & Hall.
  26. Stukel, D.M. and J.N.K. Rao. 1997. “Estimation of Regression Models with Nested Error Regression Structure and Unequal Error Variances Under Two and Three Stage Cluster Sampling.” Statistics & Probability Letters 35: 401-407. Doi: http://dx.doi.org/10.1016/S0167-7152(97)86602-3.10.1016/S0167-7152(97)86602-3
  27. Stukel, D.M. and J.N.K. Rao. 1999. “On Small-Area Estimation Under Two-Fold Nested Error Regression Models.” Journal of Statistical Planning and Inference 78: 131-147. Doi: http://dx.doi.org/10.1016/S0378-3758(98)00211-0.10.1016/S0378-3758(98)00211-0
  28. 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: 2963-2979. Doi: http://dx.doi.org/10.1016/j.jspi.2010.03.043.10.1016/j.jspi.2010.03.043
  29. Yan, G. and J. Sedransk. 2007. “Bayesian Diagnostic Techniques for Detecting Hierarchical Structure.” Bayesian Analysis 2: 735-760. Doi: http://dx.doi.org/10.1214/07-BA230.10.1214/07-BA230
  30. Yan, G. and J. Sedransk. 2010. “A Note on Bayesian Residuals as a Hierarchical Model Diagnostic Technique.” Statistical Papers 51: 1-10. Doi: http://dx.doi.org/10.1007/s00362-007-0111-2. 10.1007/s00362-007-0111-2
Language: English
Page range: 187 - 208
Submitted on: Dec 1, 2012
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Accepted on: Oct 1, 2015
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Published on: Mar 10, 2016
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2016 Balgobin Nandram, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.