Robust estimation of small-area means and quantiles

Tzavidis, Nikos, Marchetti, Stefano and Chambers, Ray (2010) Robust estimation of small-area means and quantiles. Australian & New Zealand Journal of Statistics, 52 (2), 167-186. (doi:10.1111/j.1467-842X.2010.00572.x).

Abstract

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.

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Contributors

Author: Nikos Tzavidis

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