arXiv subjects

Alicja Jokiel-Rokita

Publications and source records attributed to Alicja Jokiel-Rokita.

3 recordsLinked to original sources

arXiv2026

Estimation of quantile inequality curves and measures based on grouped data

Estimation of quantile inequality curves and measures is considered in a parametric model based on grouped data. The unknown parameters of the distribution are estimated using the minimum divergence method, using various $\phi$-divergences. The consistency of the plug-in estimators of the inequality curves and measures and the asymptotic normality of the indices estimators are proved. In a simulation study, the methods are verified and compared in terms of the accuracy of the estimation. The practical applications of the proposed methods are illustrated by the analysis of two real data sets.

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arXiv2025

Estimation of conditional inequality curves and measures via estimating the conditional quantile function

The classical concept of inequality curves and measures is extended to conditional inequality curves and measures and a curve of conditional inequality measures is introduced. This extension provides a more nuanced analysis of inequality in relation to covariates. In particular, this enables comparison of inequalities between subpopulations, conditioned on certain values of covariates. To estimate the curves and measures, a novel method for estimating the conditional quantile function is proposed. The method incorporates a modified quantile regression framework that employs isotonic regression to ensure that there is no quantile crossing. The consistency of the proposed estimators is proved while their finite sample performance is evaluated through simulation studies and compared with existing quantile regression approaches. Finally, practical application is demonstrated by analysing salary inequality across different employee age groups, highlighting the potential of conditional inequality measures in empirical research. The code used to prepare the results presented in this article is available in a dedicated GitHub repository.

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arXiv2023

Nonparametric estimators of inequality curves and inequality measures

Classical inequality curves and inequality measures are defined for distributions with finite mean value. Moreover, their empirical counterparts are not resistant to outliers. For these reasons, quantile versions of known inequality curves such as the Lorenz, Bonferroni, Zenga and $D$ curves, and quantile versions of inequality measures such as the Gini, Bonferroni, Zenga and $D$ indices have been proposed in the literature. We propose various nonparametric estimators of quantile versions of inequality curves and inequality measures, prove their consistency, and compare their accuracy in a~simulation study. We also give examples of the use of quantile versions of inequality measures in real data analysis.

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