Robust generalized linear mixed models for small area estimation

Journal of Statistical Planning and Inference

Volumn 98, Issue 1-2, 2001, Pages 225-238

  Maiti, Tapabrata ^a  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

62G35; 62J12; Hierarchical model; Improper prior; Markov Chain Monte Carlo; Partially proper prior; Posterior propriety; Small area estimation; Survey data

Indexed keywords

EID: 0041906994     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(00)00302-5     Document Type: Article

References (43)

1. Arora V., Lahiri P. On the superiority of the Bayesian method over the BLUP in small area estimation problems. Statist. Sinica. 7:1997;1053-1063.
2. Battese G.E., Harter R.M., Fuller W.A. An error-components model for prediction of county crop areas using surveys and satellite data. J. Amer. Statist. Assoc. 80:1988;28-36.
3. Besag J., Green P., Higdon D., Mengersen K. Bayesian computation and stochastic systems (with discussion). Statist. Sci. 10:1995;3-66.
4. Breslow N.E., Clayton D.G. Approximate inference in generalized linear mixed models. J. Amer. Statist. Assoc. 88:1993;9-25.
5. Carter G.M., Rolph J.E. Empirical Bayes methods applied to estimating fire alarms probabilities. J. Amer. Statist. Assoc. 69:1974;269-277.
6. Chaudhuri A. Small domain statistics: a review. Statist. Nearlandica. 48:1994;215-236.
7. Chib S., Greenberg E. Understanding the Metropolis-Hastings algorithm. Amer. Statist. 49:1995;327-335.
8. Dartigues J.F., Gagnon M., Letenneur L., Barberger-Gateau P., Commenges D., Evaldre M., Salamon R. Principle lifetime occupation and cognitive impairment in a French Elderly Cohort. Amer. J. Epidemiol. 135:1992;981-988.
9. Datta, G.S., Day, B., Basawa, I.V., 1997. Empirical best linear unbiased and empirical Bayes prediction in multivariate small area estimation. Technical Report, University of Georgia.
10. Datta G.S., Ghosh M. Bayesian prediction in linear models: applications to small area estimation. Ann. Statist. 19:1991;1748-1770.
11. Datta G.S., Lahiri P. Robust hierarchical Bayes estimation of small area characteristics in the presence of covariates and outliers. J. Multivariate Anal. 54:1995;310-328.
12. Datta, G.S., Lahiri, P., 1997. A unified measure of uncertainty of estimated best linear unbiased predictor in small-area estimation problems. Technical Report 97-7, Department of Statistics, University of Georgia.
13. Escobar M.D., West M. Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90:1995;577-588.
14. Farrell P., MacGibbon J., Tomberlin T.J. Empirical Bayes Estimators of small area proportions in multistage designs. Statist. Sinica. 7:1997;1065-1083.
15. Fay R.E., Herriot R.A. Estimates of income for small places: an application of James-Stein procedure to census data. J. Amer. Statist. Assoc. 74:1979;269-277.
16. Gelfand A., Smith A.F.M. Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85:1990;398-409.
17. Gelman A., Rubin D.B. Inference from iterative simulation using multiple sequences (with discussion). Statist. Sci. 7:1992;457-511.
18. Ghosh M., Lahiri P. Robust empirical Bayes estimation of means from stratified samples. J. Amer. Statist. Assoc. 82:1987;1153-1162.
19. Ghosh M., Lahiri P. Bayes and empirical Bayes analysis in multistage sampling. Gupta S.S., Berger J.O. Statistical Decision Theory and Related Topics IV, Vol. 1. 1992;195-212 Springer, New York.
20. Ghosh M., Meeden G. Empirical Bayes estimation in finite population sampling. J. Amer. Statist. Assoc. 81:1986;1058-1062.
21. Ghosh M., Natarajan K., Stroud T.W.F., Carlin B.P. Generalized linear models for small area estimation. J. Amer. Statist. Assoc. 93:1998;273-282.
22. Ghosh M., Rao J.N.K. Small area estimation: an appraisal (with discussion). Statist. Sci. 9:1994;55-93.
23. Ghosh J.K., Mukerjee R. Non-informative priors (with discussion). Bernado J.M.et al. Bayesian Statistics, Vol. 4. 1992;195-210 Oxford University Press, Oxford.
24. Gilks W.R., Wild P. Adaptive rejection sampling for Gibbs sampling. Appl. Statist. 41:1992;337-348.
25. Jiang, J., Lahiri, P., 1998. Empirical best prediction for small area inference with binary data. Unpublished manuscript.
26. Lahiri P., Rao J.N.K. Robust estimation of mean squared of small area estimators. J. Amer. Statist. Assoc. 90:1995;758-766.
27. Laird N.M., Louis T.A. Empirical Bayes confidence intervals based on bootstrap samples. J. Amer. Statist. Assoc. 82:1987;739-750.
28. MacGibbon B., Tomberlin T.J. Small area estimates of proportions via empirical Bayes techniques. Survey Methodol. 15:1989;33-56.
29. Maiti T. Hierarchical Bayes estimation of mortality rates for disease mapping. J. Statist. Plan. Inference. 69:1998;339-348.
30. Maiti, T., 1998b. Robust small area estimation using mixture of distributions. Unpublished manuscript.
31. Malec, D., Sedransk, J., Moriarity, C.L., Le Clere, B.F., 1997. Small area inference for binary variables in the national health interview survey. J. Amer. Statist. Assoc. 92, 815-826.
32. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equations of state calculations by fast computing machines. J. Chem. Phys. 21:1953;1087-1092.
33. Nandram B., Sedransk J. Bayesian predictive inference for a finite population proportions: two stage cluster sampling. J. Roy. Statist. Soc. Ser. B. 55:1993;399-408.
34. Nandram B., Sedransk J., Pickle L. Bayesian analysis of mortality rates for U.S. health service areas. Sankhya, B, Special Issues on Sample Surveys. 61:1999;145-165.
35. Prasad N.G.N., Rao J.N.K. The estimation of mean squared errors of small area estimators. J. Amer. Statist. Assoc. 85:1990;163-171.
36. Robert C.P. Mixture of distributions: inference and estimation. Gilks W., Richardson S., Spiegelhalter D. Practical Markov Chain Monte Carlo. 1996;441-464 Chapman & Hall, New York.
37. Roeder K., Wasserman L. Practical Bayesian density estimation using mixture of normals. J. Amer. Statist. Assoc. 92:1997;894-902.
38. Sarkar S., Ghosh M. Empirical Bayes estimation of local area means for NEF-QVF superpopulations. Sankhyǎ B. 60:1998;464-478.
39. Schaible, W.L. (Ed.), 1993. Indirect Estimators in Federal Programs. Statistical Policy Working Paper 21, Prepared by Subcommittee on Small Area Estimation, Federal Committee on Statistical Methodology, Statistical Policy Office, Office of Information and Regulatory Affairs, Office of Management and Budget.
40. Schwarz, G., 1978. Estimating the dimension of a model. The Annals of Statistics, 6, 461-464.
41. Singh A.C., Stukel D.M., Pfeffermann D. Bayesian versus frequentist measures of error in small area estimation. J. Roy. Statist. Soc. B. 60:1998;377-396.
42. Stroud T.W.F. Hierarchical Bayes predictive means and variances with application to sample survey inference. Commun. Statist. Theoret. Methods. 20:1991;13-36.
43. Stroud T.W.F. Bayesian inference from categorical survey data. Canad. J. Statist. 22:1994;33-36.