Design-based distribution function estimation for stigmatized populations

In this paper, we discuss in a general framework the design-based estimation of population parameters when sensitive data are collected by randomized response techniques. We show in close detail the procedure for estimating the distribution function of a sensitive quantitative variable and how to estimate simultaneously the population prevalence of individuals bearing a stigmatizing attribute and the distribution function for the members belonging to the hidden group. The randomized response devices by Greenberg et al. (J Am Stat Assoc 66:243–250, <CitationRef CitationID="CR21">1971</CitationRef>), Franklin (Commun Stat Theory Methods 18:489–505, <CitationRef CitationID="CR20">1989</CitationRef>), and Singh et al. (Aust NZ J Stat 40:291–297 <CitationRef CitationID="CR32">1998</CitationRef>) are here considered as data-gathering tools. Copyright Springer-Verlag Berlin Heidelberg 2013