TY - JOUR
TI - Statistical Inference for the quintile share ratio
UR - http://www.sciencedirect.com/science/article/pii/S0378375811001200
KW - inequality measure, sampling, variance, estimation, quantile, confidence intervals
LA - en
AU - Langel, M.
AU - Tillé, Y.
PY - 2011
DA - 14.3
AB - 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.
T2 - Journal of Statistical Planning and Inference
IS - 8
VL - 141
SP - 2976
EP - 2985
ER -