# A comparison of adjusted Bayes Estimators of an ensemble of small area parameters

## DOI:

https://doi.org/10.6092/issn.1973-2201/3559## Abstract

With “ensemble properties” of small area estimators, we mean their ability to reproduce the Empirical Distribution Function (EDF) characterizing the collection of underlying small area parameters (means, totals). Good “ensemble properties” may be relevant when estimation of non-linear functionals of the EDF of small area parameters (such as their variance) is needed. Small area estimators associated to the popular Fay-Herriot model are considered. “Bayes estimators”, i.e. posterior means, do not enjoy of good ensemble properties. In this paper three different adjusted predictors are compared, by means of a simulation exercise, under the assumption of correctly specified model. As the distributional assumptions on the random effects are difficult to assess, the considered predictors are compared also with respect to their robustness to the presence of failures in the distributional assumptions on the random effects.## References

T.W. ANDERSON AND D.A. DARLING (1954) A test of goodness of fit, “Journal of the American Statistical Association”, 49, pp. 765-769.

M.K. COWLES, B.P. CARLIN (1996) Markov Chain Monte Carlo convergence diagnostics: a comparative review, “Journal of the American Statistical Association”, 91, pp. 833-904.

E. FABRIZI, M.R. FERRANTE AND S. PACEI (2005) Estimation of poverty indicators at sub-national level using multivariate small area models. “Statistics in Transition”, 7, pp. 587-608.

E. FABRIZI AND C. TRIVISANO (2009) Robust Linear Mixed Models for Small Area Estimation, “Journal of Statistical Planning and Inference”, 140, 433-443.

R. FAY R. AND R.A. HERRIOT (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.

N. GANESH AND P. LAHIRI (2008), A new class of average moment matching priors, Biometrika, 95, pp. 514-520.

A. GELMAN (2006) Prior distribution for variance parameters in hierarchical models, “Bayesian Analysis”, 1, pp. 515-533.

M. GHOSH (1992) Constrained Bayes estimation with applications, Journal of the American Statistical Association, 87, 533-540.

M. GHOSH AND T. MAITI (1999) Adjusted Bayes estimators with applications to Small Area Estimation, “Sankhya”, Ser. B, 61, pp. 71-90.

H. GOLDSTEIN (1975) A Note on some Bayesian Nonparametric Estimates, “Annals of Statistics”, 3, pp. 736-740.

P. HEADY AND M. RALPHS (2004) Some findings of the EURAREA project – and their implications for statistical policy, “Statistics in Transition”, 6, pp. 641-653.

D.R. JUDKINS AND J. LIU (2000) Correcting the Bias in the Range of a Statistic across Small Areas, “Journal of Official Statistics”, 16, pp. 1-13.

P. LAHIRI, J. JIANG (2006) Mixed model prediction and small area estimation, “Test”, 15, pp. 1-96.

T.A. LOUIS (1984) Estimating a Population of Parameters Values Using Bayes and Empirical Bayes Methods, “Journal of the American Statistical Association”, 79, pp. 393-398.

J.N.K. RAO (2003) Small Area Estimation, John Wiley and Sons, New York.

R DEVELOPMENT CORE TEAM (2006) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL downloadable at http://www.R-project.org.

S. SINHARAY, H.S. STERN (2003) Posterior predictive model checking in hierarchical models, “Journal of Statistical Planning and Inference”, 111, pp. 209-221.

E. SPJØTVOLL, I. THOMSEN (1987) Application of some empirical Bayes methods to Small Area Estimation, “Bullettin of the International Statistical Institute”, 2, pp. 435-449.

A. THOMAS, B. O'HARA (2006) The BRugs package, Software and Documentation, downloadable at http://cran.r-project.org/org/packages/BRugs.

A. THOMAS, B. O HARA, U. LIGGES, S. STURZ (2006) Making BUGS Open, “R News”, 6, pp. 12-17.

L.C. ZHANG (2003) Simultaneous estimation of the mean of a binary variable from a large number of small areas, “Journal of Official Statistics”, 19, pp. 253-263.

## Downloads

## Published

## How to Cite

*Statistica*,

*69*(4), 269–284. https://doi.org/10.6092/issn.1973-2201/3559

## Issue

## Section

## License

Copyright (c) 2009 Statistica

This journal is licensed under a Creative Commons Attribution 3.0 Unported License (full legal code).

Authors accept to transfer their copyrights to the journal.

See also our Open Access Policy.