Events and Meetings of Italian Statistical Society, Statistics and Demography: the Legacy of Corrado Gini

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On the linearization of some inequality indices under the randomized response theory
Pier Francesco Perri, Giancarlo Diana

Last modified: 2015-09-05


Variance estimation of complex population parameters is a matter of primary concern in the sampling practice and linearization methods are customarily adopted. In this paper, we extend Deville's (1999) linearization approach - stemming from the concept of design-based influence function - to the case where data are supposed to be sensitive and, thus, are collected on the basis of the randomized response theory in order to reduce nonsampling errors arising from refusal to respond and/or falsification of answers.
We provide a general result for obtaining the influence function and we apply it to the Gini concentration index and the Amato index.

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