Statistical Inference for the quintile share ratio
Résumé |
In recent years, the QuintileShareRatio (or QSR) has become a very
popular measure of inequality. In 2001, the European Council
decided that income inequality in European Union member states
should be described using two indicators: the Gini Index and the
QSR. The QSR is generally defined as the ratio of the total income
earned by the richest 20% of the population relative to that earned
by the poorest 20%. Thus, it can be expressed using quantile shares,
where a quantile share is the share of total income earned by all of
the units up to a given quantile. The aim of this paper is to
propose an improved methodology for the estimation and variance
estimation of the QSR in a complex sampling design framework.
Because the QSR is a non-linear function of interest, the
estimation of its sampling variance requires advanced methodology.
Moreover, a non-trivial obstacle in the estimation of quantile
shares in finite populations is the non-unique definition of a
quantile. Thus, two different conceptions of the quantile share are
presented in the paper, leading us to two different estimators of
the QSR. Regarding variance estimation, [19] and [20] proposed a
variance estimator based on linearization techniques. However, his
method involves Gaussian kernel smoothing of cumulative
distribution functions. Our approach, also based on linearization,
shows that no smoothing is needed. The construction of confidence
intervals is discussed and a proposition is made to account for the
skewness of the sampling distribution of the QSR. Finally,
simulation studies are run to assess the relevance of our
theoretical results. |
Mots-clés |
inequality measure, sampling, variance, estimation, quantile, confidence intervals |
Citation | Langel, M., & Tillé, Y. (2011). Statistical Inference for the quintile share ratio. Journal of Statistical Planning and Inference, 141(8), 2976-2985. |
Type | Article de périodique (Anglais) |
Date de publication | 14-3-2011 |
Nom du périodique | Journal of Statistical Planning and Inference |
Volume | 141 |
Numéro | 8 |
Pages | 2976-2985 |
URL | http://www.sciencedirect.com/science/article/pii/S0378375... |