176
Views
0
CrossRef citations to date
0
Altmetric
Articles

A resampling approach to estimation of the linking variance in the Fay–Herriot model

ORCID Icon
Pages 170-177 | Received 27 Dec 2018, Accepted 30 Sep 2019, Published online: 14 Oct 2019

References

  • Barbe, P., & Bertail, P (1995). The weighted bootstrap, volume 98 of Lecture Notes in Statistics. New York, NY: Springer-Verlag.
  • Chatterjee, S. (1998). Another look at the jackknife: Further examples of generalized bootstrap. Statistics and Probability Letters, 40(4), 307–319.
  • Chatterjee, S. (2018). On modifications to linking variance estimators in the Fay-Herriot model that induce robustness. Statistics And Applications, 16(1), 289–303.
  • Chatterjee, S., & Bose, A. (2000). Variance estimation in high dimensional regression models. Statistica Sinica, 10(2), 497–516.
  • Chatterjee, S., & Bose, A. (2002). Dimension asymptotics for generalised bootstrap in linear regression. Annals of the Institute of Statistical Mathematics, 54(2), 367–381.
  • Chatterjee, S., & Bose, A. (2005). Generalized bootstrap for estimating equations. The Annals of Statistics, 33(1), 414–436.
  • Chatterjee, S., Lahiri, P., & Li, H. (2008). Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models. The Annals of Statistics, 36(3), 1221–1245.
  • Das, K., Jiang, J., & Rao, J. N. K. (2004). Mean squared error of empirical predictor. The Annals of Statistics, 32(2), 818–840.
  • Datta, G. S., Hall, P., & Mandal, A. (2011). Model selection by testing for the presence of small-area effects, and application to area-level data. Journal of the American Statistical Association, 106(493), 362–374.
  • Datta, G. S., Rao, J. N. K., & Smith, D. D. (2005). On measuring the variability of small area estimators under a basic area level model. Biometrika, 92(1), 183–196.
  • Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26.
  • Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Boca Raton, FL: Chapman & Hall/CRC press.
  • Fay III, R. E., & Herriot, R. A. (1979). Estimates of income for small places: an application of James-Stein procedures to census data. Journal of the American Statistical Association, 74(366), 269–277.
  • Hirose, M. Y., & Lahiri, P (2017). A new model variance estimator for an area level small area model to solve multiple problems simultaneously. arXiv preprint arXiv:1701.04176.
  • Jiang, J., & Lahiri, P. (2006). Mixed model prediction and small area estimation (with discussion). Test, 15(1), 1–96.
  • Jiang, J., Lahiri, P., & Wan, S.-M. (2002). A unified jackknife theory for empirical best prediction with M-estimation. The Annals of Statistics, 30(6), 1782–1810.
  • Kubokawa, T., & Nagashima, B. (2012). Parametric bootstrap methods for bias correction in linear mixed models. Journal of Multivariate Analysis, 106, 1–16.
  • Li, H., & Lahiri, P. (2010). An adjusted maximum likelihood method for solving small area estimation problems. Journal of Multivariate Analysis, 101(4), 882–892.
  • Molina, I., Rao, J. N. K., & Datta, G. S. (2015). Small area estimation under a Fay–Herriot model with preliminary testing for the presence of random area effects. Survey Methodology, 41(1), 1–19.
  • Pfeffermann, D. (2013). New important developments in small area estimation. Statistical Science, 28(1), 40–68.
  • Pfeffermann, D., & Glickman, H. (2004). Mean square error approximation in small area estimation by use of parametric and nonparametric bootstrap. ASA Section on Survey Research Methods Proceedings, Alexandria, VA, pp. 4167–4178.
  • Prasad, N. G. N., & Rao, J. N. K. (1990). The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85(409), 163–171.
  • Præstgaard, J., & Wellner, J. A. (1993). Exchangeably weighted bootstraps of the general empirical process. The Annals of Probability, 21(4), 2053–2086.
  • Rao, J. N. K. (2015). Inferential issues in model-based small area estimation: Some new developments. Statistics in Transition, 16(4), 491–510.
  • Rao, J. N. K., & Molina, I. (2015). Small area estimation. New York, NY: Wiley.
  • Rubin-Bleuer, S., & You, Y. (2016). Comparison of some positive variance estimators for the Fay–Herriot small area model. Survey Methodology, 42(1), 63–85.
  • Shao, J., & Tu, D. (1995). The jackknife and bootstrap. New York, NY: Springer-Verlag.
  • Yoshimori, M., & Lahiri, P. (2014a). A new adjusted maximum likelihood method for the Fay–Herriot small area model. Journal of Multivariate Analysis, 124, 281–294.
  • Yoshimori, M., & Lahiri, P. (2014b). A second-order efficient empirical Bayes confidence interval. The Annals of Statistics, 42(4), 1233–1261.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.