Robust Bayesian Inference in Finite Population Sampling under Balanced Loss Function

- Journal title : Communications for Statistical Applications and Methods
- Volume 21, Issue 3, 2014, pp.261-274
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2014.21.3.261

Title & Authors

Robust Bayesian Inference in Finite Population Sampling under Balanced Loss Function

Kim, Eunyoung; Kim, Dal Ho;

Kim, Eunyoung; Kim, Dal Ho;

Abstract

In this paper we develop Bayes and empirical Bayes estimators of the finite population mean with the assumption of posterior linearity rather than normality of the superpopulation under the balanced loss function. We compare the performance of the optimal Bayes estimator with ones of the classical sample mean and the usual Bayes estimator under the squared error loss with respect to the posterior expected losses, risks and Bayes risks when the underlying distribution is normal as well as when they are binomial and Poisson.

Keywords

Balanced loss function;Bayes risk;empirical Bayes;finite population mean;posterior expected loss;posterior linearity;risk function;

Language

English

Cited by

References

1.

Bolfarine, H. and Zacks, S. (1992). Prediction Theory for Finite Populations, Springer-Verlag, New York.

2.

Diaconis, P. and Ylvisaker, D. (1979). Conjugate priors for exponential families. The Annals of Statistics, 7, 269-281.

3.

Ericson, W. A. (1969). Subjective Bayesian models in sampling finite populations (with discussion), Journal of the Royal Statistical Society, Series B, 31, 195-233.

4.

Ericson, W. A. (1988). Bayesian inference in finite populations. Handbook of Statistics, Vol. 6 : Sampling, Eds. P.R. Krishnaiah and C.R. Rao, North-Holland, Amsterdam, 213-246.

5.

Ghosh, M., Kim, M. J. and Kim, D. H. (2008). Constrained Bayes and empirical Bayes estimation under random effects normal ANOVA model with balanced loss function, Journal of Statistical Planning and Inference, 138, 2017-2028.

6.

Ghosh, M. and Lahiri, P. (1987). Robust empirical Bayes estimation of means from stratified samples, Journal of the American Statistical Association, 82, 1153-1162.

7.

Ghosh, M. and Meeden, G. (1986). Empirical Bayes estimation in finite population sampling, Journal of the American Statistical Association, 81, 1058-1062.

8.

Ghosh, M. and Meeden, G. (1997). Bayesian Methods for Finite Population Sampling, Chapman and Hall, London.

9.

Goldstein, M. (1975). A note on some Bayesian nonparametric estimates, The Annals of Statistics, 3, 736-740.

10.

Hartigan, J. A. (1969). Linear Bayes methods, Journal of the Royal Statistical Society, Series B, 31, 446-454.

11.

Hill, B. (1968). Posterior distribution of percentiles: Bayes theorem for sampling from a population. Journal of the American Statistical Association, 63, 677-691.

12.

Mukhopadhyay, P. (2000). Topics in Survey Sampling, Springer-Verlag, New York.

13.

Royall, R. M. and Cumberland,W. G. (1981). An empirical study of the ratio estimator and estimators of its variance (with discussion). Journal of the American Statistical Association, 76, 66-88.

15.

Zellner, A. (1992). Bayesian and Non-Bayesian Estimation Using Balanced Loss Functions. In Statistical Decision Theory and Related Topics V. Eds. S.S. Gupta and J.O. Berger, Springer-Verlag, New York, 377-390.