Gini index estimation in randomized response surveys

In this paper, we address the problem of estimating the Gini index when data are assumed to be collected through the randomized response method proposed by Greenberg et al.(1971). In the design-based framework, we treat the Gini index as a population functional and follow the approach proposed by Deville (1999) to obtain the corresponding estimator. Variance estimation is also considered. A simulation study is carried out by using real income data from the \textit{Survey of Household Income and Wealth} conducted by the Bank of Italy (2010) in order to assess the performance of the proposed estimators.