An application of the interval estimation for the At-Risk-of-Poverty Rate assessment

In the document [Eurostat (Your Key to European Statistics) 2020], At-Risk-of-Poverty Rate (ARPR in short) is defined as the percentage of population with an income not exceeding 60% of the general population median income. Extensive and thorough research on the estimation of this measure has been conducted since its introduction. For example, in the paper of [Zieliński 2009a] a non-parametric, distribution-free confidence interval for ARPR has been constructed. An example of application of the confidence interval proposed by [Zieliński 2009a] has been given in [Zieliński 2009b]. Some other interesting approach regarding the interval estimation of ARPR has been proposed in [Luo and Qin 2017], where the authors introduced new concepts of the interval estimation for the so-called Low-Income Proportion (LIP) measure, which is a generalization of ARPR. The LIP measure and thus, the ARPR parameter in particular, are important indexes describing the inequality in an income distribution. Based on the construction of the point smoothed kernel estimate for LIP, [Luo and Qin 2017] established a smoothed jackknife empirical likelihood approach leading to the introduction of some new non-parametric confidence intervals for the LIP measure and consequently, for the ARPR index as well. In our work, we aim to apply the most interesting ideas of LIP and ARPR point and interval estimation for data consisting of observations concerning an equalised disposable income of households in Poland from 2003. We also discuss the accuracy and adequacy of the empirical results relating to the ARPR interval estimation, obtained by the implementation of the constructed confidence intervals.