Social Statistics and Centre for Census and Survey Research, University of Manchester, Manchester M13 9PL, UK. e-mail: email@example.com
ROBUST ESTIMATION OF SMALL-AREA MEANS AND QUANTILES
Version of Record online: 19 APR 2010
© 2010 Australian Statistical Publishing Association Inc.
Australian & New Zealand Journal of Statistics
Volume 52, Issue 2, pages 167–186, June 2010
How to Cite
Tzavidis, N., Marchetti, S. and Chambers, R. (2010), ROBUST ESTIMATION OF SMALL-AREA MEANS AND QUANTILES. Australian & New Zealand Journal of Statistics, 52: 167–186. doi: 10.1111/j.1467-842X.2010.00572.x
Acknowledgements. The research described in this paper was supported in part by ARC Linkage Grant LP0776810 of the Australian Research Council and by a 7th European Framework Grant SSH-CT-2008-217565 FP7-SSH-2007-1 of the European Commission. We are grateful to the Technical Editor for suggestions that considerably improved the paper.
- Issue online: 25 MAY 2010
- Version of Record online: 19 APR 2010
- Australian farm data;
- Chambers–Dunstan estimator;
- finite-population distribution function;
- M-quantile regression;
- Rao–Kovar–Mantel estimator;
- robust regression;
- small-area estimation;
- smearing estimator
Small-area estimation techniques have typically relied on plug-in estimation based on models containing random area effects. More recently, regression M-quantiles have been suggested for this purpose, thus avoiding conventional Gaussian assumptions, as well as problems associated with the specification of random effects. However, the plug-in M-quantile estimator for the small-area mean can be shown to be the expected value of this mean with respect to a generally biased estimator of the small-area cumulative distribution function of the characteristic of interest. To correct this problem, we propose a general framework for robust small-area estimation, based on representing a small-area estimator as a functional of a predictor of this small-area cumulative distribution function. Key advantages of this framework are that it naturally leads to integrated estimation of small-area means and quantiles and is not restricted to M-quantile models. We also discuss mean squared error estimation for the resulting estimators, and demonstrate the advantages of our approach through model-based and design-based simulations, with the latter using economic data collected in an Australian farm survey.