DOI QR코드

DOI QR Code

Bayesian small area estimations with measurement errors

  • Goo, You Mee (Department of Statistics, Kyungpook National University) ;
  • Kim, Dal Ho (Department of Statistics, Kyungpook National University)
  • Received : 2013.05.06
  • Accepted : 2013.05.21
  • Published : 2013.07.31

Abstract

This paper considers Bayes estimations of the small area means under Fay-Herriot model with measurement errors. We provide empirical Bayes predictors of small area means with the corresponding jackknifed mean squared prediction errors. Also we obtain hierarchical Bayes predictors and the corresponding posterior standard deviations using Gibbs sampling. Numerical studies are provided to illustrate our methods and compare their eciencies.

Keywords

References

  1. Bolfarine, H., Zacks, S. and Sandoval, M. (1996). On predicting the population total under regression models with measurement errors. Journal of Statistical Planning and Inference, 55, 63-76. https://doi.org/10.1016/0378-3758(95)00181-6
  2. Cheng, C. L. and Van Ness, J. W. (1999). Statistical regression with measurement error, Arnold, London.
  3. 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.
  4. Datta, G. S., Rao, J. N. K. and Smith, D. D. (2005). On measuring the validity of small area estimators under a basic area level model. Biometrika, 92, 183-196. https://doi.org/10.1093/biomet/92.1.183
  5. Datta, G. S., Rao, J. N. K. and Torabi, M. (2010). Pseudo-empirical Bayes estimation of small area means under a nested error linear regression model with functional measurement errors. Journal of Statistical Planning and Inference, 140, 2952-2962. https://doi.org/10.1016/j.jspi.2010.03.046
  6. Fay, R. E. and 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, 269-277.
  7. Ghosh, M. and Sinha, K. (2007). Empirical Bayesian estimation in nite population sampling under functional measurement error model. Journal of Statistical Planning and Inference, 137, 2759-2773. https://doi.org/10.1016/j.jspi.2006.08.008
  8. Ghosh, M., Sinha, K. and Kim, D. (2006). Empirical and hierarchical Bayesian estimation in finite population sampling under structural measurement error model. The Scandinavian Journal of Statistics, 33, 591-608. https://doi.org/10.1111/j.1467-9469.2006.00492.x
  9. Goo, Y. M. and Kim, D. H. (2012). Bayesian inference in finite population sampling under measurement error model. Journal of the Korean Data & Information Science Society, 23, 1241-1247. https://doi.org/10.7465/jkdi.2012.23.6.1241
  10. Jiang, J., Lahiri, P. and Wan, S.M. (2002) A unfiied Jackknife theory for empirical best prediction with M-estimation. Annals of Statistics, 30, 1782-1810. https://doi.org/10.1214/aos/1043351257
  11. 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. https://doi.org/10.1080/01621459.1990.10475320
  12. Rao, J. N. K. (2003). Small area estimation, Wiley, New York.
  13. Torabi, M., Datta, G. S. and Rao, J. N. K. (2009). Empirical Bayes estimation of small area means under a nested error linear regression model with measurement errors in the covariates. The Scandinavian Journal of Statistics, 36, 355-368. https://doi.org/10.1111/j.1467-9469.2008.00623.x
  14. Ybarra, L. M. R. and Lohr, S. L. (2008). Small area estimation when auxiliary information is measured with error. Biometrika, 95, 919-931. https://doi.org/10.1093/biomet/asn048

Cited by

  1. Bayesian estimation of median household income for small areas with some longitudinal pattern vol.26, pp.3, 2015, https://doi.org/10.7465/jkdi.2015.26.3.755
  2. Bayesian curve-fitting with radial basis functions under functional measurement error model vol.26, pp.3, 2015, https://doi.org/10.7465/jkdi.2015.26.3.749
  3. Simultaneous modeling of mean and variance in small area estimation vol.27, pp.5, 2016, https://doi.org/10.7465/jkdi.2016.27.5.1423
  4. Bayesian smoothing under structural measurement error model with multiple covariates vol.28, pp.3, 2017, https://doi.org/10.7465/jkdi.2017.28.3.709