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).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1111/j.1467-842X.2010.00572.x
ISSNs: 1369-1473 (print)
1467-842X (electronic)
Keywords: australian farm data, chambers–dunstan estimator, finite-population distribution function, m-quantile regression, rao–kovar–mantel estimator, robust regression, small-area estimation, smearing estimator
Subjects: H Social Sciences > HA Statistics
S Agriculture > S Agriculture (General)
Divisions : University Structure - Pre August 2011 > School of Social Sciences > Social Statistics
ePrint ID: 181889
Accepted Date and Publication Date:
June 2010Published
Date Deposited: 19 Apr 2011 14:40
Last Modified: 31 Mar 2016 13:36

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