Empirical Likelihood Confidence Intervals: An Application to the EU-SILC Household Surveys

Abstract

Berger and De La Riva Torres (2012), proposed a proper empirical likelihood approach which can be used to construct design-based confidence intervals. The proposed approach gives confidence intervals which may have better coverages than standard confidence intervals, which relies on normality, variance estimates and linearisation. The proposed approach does not rely on variance estimates, re-sampling or linearisation, even when the point estimator is not linear and does not have a normal distribution. It can be also used to construct confidence intervals of means, regressions coefficients, quantiles and poverty indicators. The proposed approach is less computational intensive than rescaled bootstrap (Rao and Wu 1988) which can be unstable and may not have the intended coverages (Berger and De La Riva Torres 2012). We apply the proposed approach to a measure of poverty based upon the European Union Statistics on Income and Living Conditions (eu-silc) survey (Eurostat 2012). Confidence intervals of the persistent-risk-of-poverty indicator are estimated for the overall population and six sub-population domains determined by cross-classifying age groups and gender. This work was supported by consulting work for the Net-SILC2 project (Atkinson and Marlier 2010).