Empirical bootstrap bias correction and estimation of prediction mean square error in small area estimation

Biometrika

Volumn 99, Issue 2, 2012, Pages 457-472

  Pfeffermann, D ^a   Correa, S ^b  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA   (Brazil)

Author keywords

Best predictor; Crossvalidation; Empirical best predictor; Generalized mixed model; Jackknife; Order of bias; Parametric bootstrap

Indexed keywords

EID: 84861630556     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/ass010     Document Type: Article

References (17)

1. CANTY, A. J., DAVISON, A. C., HINKLEY, D. V. & VENTURA, V. (2006). Bootstrap diagnostics and remedies. Can. J. Statist. 34, 5-27.
2. DATTA, G. S. (2009).Model-based approach to small area estimation. In Handbook of Statistics 29B, Sample Surveys: Inference and Analysis, Ed. D. Pfeffermann and C. R. Rao, pp. 251-88. North Holland: Elsevier.
3. DAVIS, P. J. & RABINOWITZ, P. (1984). Methods of Numerical Integration. Computer Science and Applied Mathematics, 2nd edn. Orlando: Academic Press.
4. DAVISON, A. C. & HINKLEY, D. V. (1997). Bootstrap Methods and their Application. Cambridge: Cambridge University Press.
5. EFRON, B. (1982). The Jackknife, the Bootstrap and other Resampling Plans. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
6. EFRON, B. & TIBSHIRANI, R. J. (1993). An Introduction to the Bootstrap. New York: Chapman & Hall.
7. FAY, R. E. & HERRIOT, R. (1979). Estimates of income for small places: an application of James-Stein procedures to census data. J. Am. Statist. Assoc. 74, 269-77.
8. FIRTH, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika 80, 27-38.
9. HALL, P. & MAITI, T. (2006). On parametric bootstrap methods for small area prediction. J. R. Statist. Soc. B 68, 221-38.
10. HALL, P. & MARTIN, M. A. (1988). On bootstrap resampling and iteration. Biometrika 75, 661-71.
11. JIANG, J. & LAHIRI, P. (2006). Mixed model prediction and small area estimation. Test 15, 1-96.
12. JIANG, J., JAHIRI, P.&WAN, S. M. (2002). A unified jackknife theory for empirical best prediction withM-estimation. Ann. Statist. 30, 1782-810.
13. LOHR, S. L. & RAO, J. N. K. (2009). Jackknife estimation of mean squared error of small area predictors in nonlinear mixed models. Biometrika 96, 457-68.
14. R DEVELOPMENT CORE TEAM. (2012). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0. URL http://www.R-project.org.
15. RAO, J. N. K. (2003). Small Area Estimation. New York: Wiley.
16. TIBSHIRANI, R. J. (1988). Variance stabilization and the bootstrap. Biometrika 75, 433-44.
17. TIERNEY, L. & KADANE, J. (1986). Accurate approximations for posterior moments and marginals. J. Am. Statist. Assoc. 81, 82-6.