Résultat de la recherche
On measuring income inequality
L'inégalité des revenus est un sujet profond. Ma recherche ne vise en aucun cas à couvrir tous les aspects du sujet. À mon humble avis, la compréhension de l'inégalité des revenus, en dehors de la recherche statistique, nécessite une étude approfondie de la société humaine, de l'histoire et de la philosophie. Les statistiques n'aident pas à résoudre les questions d'inégalité des revenus en soi. Néanmoins, les statistiques fournissent une approche pour la mesurer. Cette recherche doctorale se concentre sur les questions relatives à la mesure de l'inégalité des revenus. Elle se concentre sur l'objectivité des mesures de l'inégalité des revenus, la précision de leur estimation et la quantification de l'incertitude de l'estimation. ABSTRACT Income inequality is a profound subject. My research by no means aims to cover every aspect of the subject. Comprehending income inequality, in my humble opinion, apart from statistical research, requires a deep investigation of human society, history and philosophy. Statistics does not help solve the questions of income inequality per se. Nevertheless, statistics provides an approach to measure it. This PhD research concentrates on the questions of measuring income inequality. It focuses on the objectivity of the income inequality measures, the accuracies of the estimation of them and the quantifications of the uncertainty of the estimation.
Linearization and Variance Estimation of the Bonferroni Inequality Index
The study of income inequality is important for predicting the wealth of a country. There is an increasing number of publications where the authors call for the use of several indices simultaneously to better account for the wealth distribution. Due to the fact that income data are usually collected through sample surveys, the sampling properties of income inequality measures should not be overlooked. The most widely used inequality measure is the Gini index, and its inferential aspects have been deeply investigated. An alternative inequality index could be the Bonferroni inequality index, although less attention on its inference has been paid in the literature. The aim of this paper is to address the inference of the Bonferroni index in a finite population framework. The Bonferroni index is linearized by differentiation with respect to the sample indicators which allows for conducting a valid inference. Furthermore, the linearized variables are used to evaluate the effects of the different observations on the Bonferroni and Gini indices. The result demonstrates once for all that the former is more sensitive to the lowest incomes in the distribution than the latter.