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IPS246 Tiziana Laureti et al.
design, the weighting procedure, the imputation schemes and the
nonlinear form of survey estimators should be reflected in the calculation
of standard errors and confidence intervals (Goedemé, 2013).
a. Estimating standard errors: An Empirical analysis for Italian regions
In Italy, EU-SILC is conducted by ISTAT to produce estimates of the
Italian population living conditions at national and also at regional level
(NUTS-2). In the design of the EU-SILC survey, regions are planned
domains for which estimates are published but without confidence
intervals (ISTAT, 2018). The regional samples are based on a stratified
two-stage sample design: in each province, municipalities are the
Primary Sampling Units (PSUs), while households are the Secondary
Sampling Units (SSUs). The PSUs are stratified according to
administrative regions and population size while SSUs are selected by
using systematic sampling. We calculate confidence intervals for the
AROP for Italian regions in 2017 (NUTS-2) using data from IT-SILC
provided by ISTAT for carrying out research projects in collaboration
with the Dagum /Tuscan Universities Research Centre on Advanced
Statistics for the Equitable and Sustainable Development.
AROP is a complex statistic since it is based on a poverty threshold
computed from the median of the income distribution, that is: =
( < 0.6 ∙ 0.5 ) ∙ 100. Therefore, the at-risk-of-poverty threshold (ARPT)
needs to be estimated first, which is set at 60% of the national median
̂
equivalized disposable income, = 0.6 ∙ 0.5 . Then the AROP rate is
defined as the proportion of persons with an equivalized disposable
̂
̂
income below the ARPT: = ∑ ∈< ∙ 100
∑
Consequently, there exist two main sources of variability: one is due
to the estimated threshold and the other one comes from the estimated
proportion given the estimated threshold (e.g., Berger and Skinner 2003;
Verma et al 2012). We used a generalized linearization method based
on the concept of influence Function (Deville, 1999) which allows us to
deal with nonlinear statistics for which the Taylor method cannot be
used. This approach does not involve more calculations.
We linked household and personal data (H, R, P D files). Household
income is equivalised using the modified OECD equivalence scale by
assuming that the living standard of all household members is the same.
Confidence intervals are estimated using linearization on the basis of
complete sample design information regarding “Primary strata”, “PSUs”,
“SSU”. The estimates are obtained using R package laeken and the DASP
module. Since a region coincides with a sample “design domain” and the
regional AROP depends only on units within region, variance

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