Model selection by testing for the presence of small-area effects, and application to area-level data

Journal of the American Statistical Association

Volumn 106, Issue 493, 2011, Pages 362-374

  Datta, Gauri S ^a   Hall, Peter ^b   Mandal, Allabhyuday ^a  

^a UNIVERSITY OF GEORGIA   (United States)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Bootstrap; Confidence intervals; Cumulants; Estimating equation; Mean squared error; P value

Indexed keywords

EID: 79954518929     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2011.tm10036     Document Type: Article

References (36)

1. Battese, G. E., Harter, R. M., and Fuller, W. A. (1988), ''An Error ComponentsModel for Prediction of County Crop Area Using Survey and Satellite Data,'' Journal of the American Statistical Association, 83, 28-36. [362]
2. Bell, W. R. (2008), ''Examining Sensitivity of Small Area Inferences to Uncertainty About Sampling Error Variances,'' in Proceedings of Section on Survey Research Methods, Joint Statistical Meetings 2008, Denver, Colorado; Alexandria, VA: American Statistical Association, pp. 327-333. [362]
3. Bell, W. R., and Huang, E. T. (2006), ''Using the t-Distribution to Deal With Outliers in Small Area Estimation,'' in Proceedings of Statistics Canada Symposium 2006: Methodological Issues in Measuring Population Health, Gatineau, Quebec, Canada; Ottawa, Ontario: Statistics Canada. [369]
4. Chatterjee, S., Lahiri, P., and Li, H. (2008), ''Parametric Bootstrap Approximation to the Distribution of EBLUP, and Related Prediction Intervals in Linear Mixed Models,'' The Annals of Statistics, 36, 1221-1245. [362]
5. Datta, G. S. (2009), ''Model-Based Approach to Small Area Estimation,'' in Handbook of Statistics: Sample Surveys: Inference and Analysis, Vol. 29B, eds. D. Pfeffermann and C. R. Rao, Amsterdam, The Netherlands: North- Holland, pp. 251-288. [362]
6. Datta, G. S., and Ghosh, M. (1991), ''Bayesian Prediction in Linear Models: Applications to Small Area Estimation,'' The Annals of Statistics, 19, 1748-1770. [362]
7. Datta, G. S., and Lahiri, P. (2000), ''A Unified Measure of Uncertainty of Estimated Best Linear Unbiased Predictors in Small Area Estimation Problems,'' Statistica Sinica, 10, 613-627. [362]
8. Farrell, P. J., MacGibbon, B., and Tomberlin, T. J. (1997), ''Empirical Bayes Estimators of Small Area Proportions in Multistage Designs,'' Statistica Sinica, 7, 1065-1083. [366]
9. Fay, R. E., and Herriot, R. A. (1979), ''Estimates of Income for Small Places: An Application of James-Stein Procedure to Census Data,'' Journal of the American Statistical Association, 74, 269-277. [362,368]
10. Ghosh, M., and Maiti, T. (2004), ''Small Area Estimation Based on Natural Exponential Family Quadratic Variance Function Models and Survey Weights,'' Biometrika, 91, 95-112. [362,363,365,366]
11. Ghosh, M., and Rao, J. N. K. (1994), ''Small Area Estimation: An Appraisal'' (with discussion), Statistical Science, 9, 55-93. [362]
12. Godambe, V. P., and Thompson, M. E. (1989), ''An Extension of Quasi-Likelihood Estimation,'' Journal of Statistical Planning and Inference, 22, 137-152. [364,365]
13. Hall, P., and Maiti, T. (2006a), ''Nonparametric Estimation of Mean-Squared Prediction Error in Nested-Error Regression Models,'' The Annals of Statistics, 34, 1733-1750. [362]
14. Hall, P., and Maiti, T. (2006b), ''On Parametric Bootstrap Methods for Small-Area Prediction,'' Journal of the Royal Statistical Society, Ser. B, 68, 221-238. [362]
15. Jiang, J., and Lahiri, P. S. (2001), ''Empirical Best Prediction for Small Area Inference With Binary Data,'' Annals of the Institute of Statistical Mathematics, 53, 217-243. [366]
16. Jiang, J., and Lahiri, P. S. (2006), ''Mixed Model Prediction and Small Area Estimation,'' Test, 15, 1-96. [362]
17. Jiang, J., and Rao, J. S. (2003), ''Consistent Procedures for Mixed Linear Model Selection,'' Sankhya, 65, 23-42. [363]
18. Jiang, J., and Tang, E. (2011), ''The Best EBLUP in the Fay-Herriot Model,'' Annals of the Institute of Statistical Mathematics, to appear. [368]
19. Jiang, J., Nguyen, T., and Rao, J. S. (2010), ''Fence Method for Nonparametric Small Area Estimation,'' Survey Methodology, 36, 3-11. [363,368]
20. Jiang, J., Rao, J. S., Gu, Z., and Nguyen, T. (2008), ''Fence Methods for Mixed Model Selection,'' The Annals of Statistics, 36, 1669-1692. [363]
21. Li, H., and Lahiri, P. (2010), ''An Adjusted Maximum Likelihood Method for Solving Small Area Estimation Problems,'' Journal of Multivariate Analysis, 101, 882-892. [362]
22. Macgibbon, B., and Tomberlin, T. J. (1989), ''Small Area Estimates of Proportions via Empirical Bayes Techniques,'' Survey Methodology, 15, 237-252. [366]
23. Morris, C. N. (1982), ''Natural Exponential Families With Quadratic Variance Functions,'' The Annals of Statistics, 10, 65-80. [362]
24. Morris, C. N. (1983), ''Natural Exponential Families With Quadratic Variance Functions: Statistical Theory,'' The Annals of Statistics, 11, 515-529. [362]
25. Morris, C. N., and Christiansen, C. L. (1995), ''Hierarchical Models for Ranking and for Identifying ExtremesWith Applications,'' in Bayesian Statistics, Vol. 5, eds. J. M. Bernardo, J. O. Bereger, A. P. Dawid, and A. F. M. Smith, New York: Oxford Univ. Press. [368]
26. Pfeffermann, D. (2002), ''Small Area Estimation: New Developments and Directions,'' International Statistical Review, 70, 125-143. [362]
27. Pfeffermann, D., and Correa, S. (2009), ''New Bootstrap Bias Corrections With Application to Estimation of Prediction MSE in Small Area Estimation,'' preprint, Southampton Statistical Sciences Research Institute, University of Southampton, Southampton, United Kingdom. [366]
28. Pfeffermann, D., Skinner, C. J., Holmes, D. J., Goldstein, H., and Rasbash, J. (1998), ''Weighting for Unequal Selection Probabilities in Multilevel Models,'' Journal of the Royal Statistical Society, Ser. B, 60, 23-40. [362]
29. Prasad, N. G. N., and Rao, J. N. K. (1990), ''The Estimation of Mean Squared Error of Small Area Estimators,'' Journal of the American Statistical Association, 85, 163-171. [362,369]
30. Prasad, N. G. N., and Rao, J. N. K. (1999), ''On Robust Small Area Estimation Using a Simple Random Effects Model,'' Survey Methodology, 25, 67-72. [362]
31. Rao, J. N. K. (1999), ''Some Recent Advances in Model-Based Small Area Estimation,'' Survey Methodology, 25, 175-186. [362]
32. Rao, J. N. K. (2003), Small Area Estimation, New York: Wiley. [362]
33. Rao, J. N. K. (2006), ''Inferential Issues in Small Area Estimation: Some New Developments,'' Statistics in Transition, 7, 513-526. [362]
34. Singh, A. C., Stukel, D. M., and Pfeffermann, D. (1998), ''Bayesian versus Frequentist Measures of Error in Small Area Estimation,'' Journal of the Royal Statistical Society, Ser. B, 60, 377-396. [362]
35. You, Y., and Rao, J. N. K. (2002), ''A Pseudo-Empirical Best Linear Unbiased Prediction Approach to Small Area Estimation Using SurveyWeights,'' Canadian Journal of Statistics, 30, 431-439. [362]
36. You, Y., and Rao, J. N. K. (2003), ''Pseudo-Hierarchical Bayes Small Area Estimation Combining Unit Level Models and SurveyWeights,'' Journal of Statistical Planning and Inference, 111, 197-208. [362]