Small Area Estimation for Poverty Indicators under Outlier Contamination
Risto Lehtonen1, Ari Veijanen2
1Department of Social Research, University of Helsinki, Helsinki, Finland; 2Statistics Finland, Helsinki, Finland

The paper discusses estimators for selected monetary poverty indicators (so-called Laeken indicators of the EU) for population subgroups or domains and small areas. The complete set of indicators includes at-risk-of poverty rate, relative median at-risk-of poverty gap (poverty gap for short), quintile share ratio (S20/S80 ratio) and the Gini coefficient. We concentrate here on quintile share and poverty gap. Both indicators rely on medians or quantiles of the cumulative distribution function of the underlying equivalized income variable.

Design-based direct, model-based indirect and composite estimators of the indicators were investigated. Linear mixed models with area-specific random intercepts were fitted for the (transformed) income variable. In our simulation studies, direct estimators were inefficient, and more efficient indirect prediction-type estimators tended to be seriously biased. We developed alternative, less biased indirect estimators called expanded prediction estimators. They showed good accuracy properties and were less affected by outlier contamination. Composite estimators were constructed as a linear combination of a direct estimator and an indirect expanded prediction estimator. With respect to bias and accuracy, composite estimators offered a good compromise.

We show results on a new technique called frequency-calibrated prediction method, aimed for situations where area-level auxiliary data only are available. A composite frequency calibrated estimator performed well with respect to bias and accuracy. This holds for quintile share in particular.

The relative performance of estimators (design bias and accuracy) was examined with design-based simulation experiments. Equal and unequal probability sampling designs were covered. We also discuss the properties of the estimators under outlier contamination. In the experiments we used unit-level and aggregate-level auxiliary data obtained from statistical registers maintained by Statistics Finland. Research has been conducted in the context of the AMELI project (Advanced Methodology for European Laeken Indicators), which is supported by European Commission funding from the Seventh Framework Programme for Research.

Keywords: Poverty indicators; Small area estimation; Mixed models; Outlier contamination

Biography: Risto Lehtonen works as Professor of Statistics at Department of Social Research of University of Helsinki. He also works as Research Professor at the Social Insurance Institution of Finland. Prof. Lehtonen is an elected member of the ISI.