Robust estimation of small-area means and quantiles

Nikos Tzavidis, Stefano Marchetti, Ray Chambers

Research output: Contribution to journalArticlepeer-review


Summary: 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. © 2010 Australian Statistical Publishing Association Inc.
Original languageEnglish
Pages (from-to)167-186
Number of pages19
JournalAustralian & New Zealand Journal of Statistics
Issue number2
Publication statusPublished - Jun 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


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