Yong You https://orcid.org/0009-0000-8030-1484

© Yong You. Article available under the CC BY-SA 4.0 licence

ARTICLE

(English) PDF

ABSTRACT

In this paper, we study hierarchical Bayes (HB) estimators based on different priors for small area estimation. In particular, we use inverse gamma and flat priors for variance components in the HB small area models of You and Chapman (2006) and You (2021). We evaluate the HB estimators through a simulation study and real data analysis. Our results indicate that using the inverse gamma prior for the variance components in the HB models can be very effective.

KEYWORDS

CPO, flat prior, inverse gamma prior, relative error, variance component

REFERENCES

Dass, S. C., Maiti,T., Ren, H. and Sinha, S., (2012). Confidence interval estimation of small area parameters shrinking both means and variances. Survey Methodology, 38, pp. 173–187.

Fay, 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, pp. 269–277.

Gelman, A., (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 1, pp. 515–533.

Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B., (2004). Bayesian Data Analysis. 2nd Edition, Chapman & Hall/CRC.

Ghosh, M., Myung, J. and Moura, F. A. S., (2018). Robust Bayesian small area estimation. Survey Methodology, 44, pp. 101–115.

Gilks, W. R., Richardson, S. and Spiegelhalter, D. J., (1996). Markov Chain Monte Carlo in Practice. Chapman & Hall/CRC.

Hidiroglou, M. A., Beaumont, J.-F. and Yung, W., (2019). Development of a small area estimation system at Statistics Canada. Survey Methodology, 45, pp. 101–126.

Lahiri, P., Rao, J. N. K., (1995). Robust estimation of mean squared error of small area estimators. Journal of the American Statistical Association, 82, pp. 758–766.

Lunn, D. J., Thomas, A., Best, N. and Spiegelhalter, D. J., (2000). WinBUGS – A Bayesian modeling framework: concepts, structure and extensibility. Statistics and Computing, 10, pp. 325–337.

Molina, I, Nandram, B. and Rao, J. N. K., (2014). Small area estimation of general parameters with application to poverty indicators: A hierarchical Bayes approach, Annals of Applied Statistics, 8, pp. 852–885.

Rao, J. N. K., Molina, I., (2015). Small Area Estimation, 2nd Edition. John Wiley & Sons, New York.

Rivest, L. P., Vandal, N. (2002). Mean squared error estimation for small areas when the small area variances are estimated. Proceedings of the International Conference on Recent Advances in Survey Sampling, July 10–13, 2002, Ottawa, Canada.

Sugasawa, S., Tamae, H. and Kubokawa, T., (2017). Bayesian estimators for small area models shrinking both means and variances. Scandinavian Journal of Statistics, 44, pp. 150–167.

You, Y., (2008). An integrated modeling approach to unemployment rate estimation for sub-provincial areas of Canada. Survey Methodology, 34, pp. 19–27.

You, Y., (2016). Hierarchical Bayes sampling variance modeling for small area estimation based on area level models with applications. Methodology branch working paper, ICCSMD-2016-03-E, Statistics Canada, Ottawa, Canada.

You, Y., (2021). Small area estimation using Fay-Herriot model with sampling variance smoothing and modeling. Survey Methodology, 47, pp. 361–370.

You, Y., Chapman, B., (2006). Small area estimation using area level models and estimated sampling variances. Survey Methodology, 32, pp. 97–103.

You, Y., Rao, J. N. K., (2000). Hierarchical Bayes estimation of small area means using multi-level models. Survey Methodology, 26, pp. 173–181.

Back to top
© 2019–2024 Copyright by Statistics Poland, some rights reserved. Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0) Creative Commons — Attribution-ShareAlike 4.0 International — CC BY-SA 4.0