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Tillé, Yves

Nom
Tillé, Yves
Affiliation principale
Site web
Fonction
Professeur ordinaire
Email
yves.tille@unine.ch
Identifiants
https://libra.unine.ch/handle/123456789/541
_
0000-0003-0904-5523

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  • Publication
    Accès libre
    Linearization and Variance Estimation of the Bonferroni Inequality Index
    (Neuchâtel Institut de Statistique Faculté des sciences, 2021)
    Dong, Ziqing 
    ;
    Tillé, Yves 
    ;
    Giorgi, Giovanni M.
    ;
    Guandalini, Alessio
    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.
  • Publication
    Métadonnées seulement
    Imputation of income data with generalized calibration procedure and GB2 law: illustration with SILC data
    (2013-8-31)
    Graf, Eric 
    ;
    Tillé, Yves 
    In sample surveys of households and persons, questions about income are often sensitive and thus subject to a higher non-response rate. Nevertheless, the household or personal incomes are among the important variables in surveys of this type. The distribution of such collected incomes is not normal, neither log-normal. Hypotheses of classical regression models to explain the income (or their log) are not fulfilled. Imputations using such models modify the original and true distribution of the data. This is not suitable and may conduct the user to wrong interpretations of results computed from data imputed in this way. The generalized beta distribution of the second kind (GB2) is a four parameters distribution. Empirical studies have shown that it adapts very well to income data. The advantage of a parametric income distribution is that there exist explicit formulae for the inequality measures like the Laeken indicators as functions of the parameters. We present a parametric method of imputation, based on the fit of a GB2 law on the income distribution by the use of suitably adjusted weights obtained by generalized calibration. These weights can compensate for non ignorable non-response that affects the variable of interest. We validate our imputation system on data from the Swiss Survey on Income and Living Conditions (SILC).