Variance Estimation by Linearisation for the At Risk of Poverty or Social Exclusion (AROPE) Rate

Abstract

The At Risk of Poverty or Social Exclusion (AROPE) Rate is the key indicator for monitoring the European Commissions 2020 Strategy poverty target. But the variance of the AROPE Rate is not straightforward to estimate. Re-sampling methods can be used, but they are difficult to adapt to complex sampling design, that are often used for the surveys that provide the data source for estimating the AROPER. The presented work fills a methodological gap by providing a linearisation of the AROPE Rate estimator that can be used with well known variance estimators and therefore facilitate the reporting of appropriate inference for this important indicator. The precision of the developed variance estimators based on linearisation is assessed via simulation studies and compared with a bootstrap variance estimator, as an alternative.