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Design-based distribution function estimation for stigmatized populations

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  • Lucio Barabesi
  • Giancarlo Diana
  • Pier Perri

Abstract

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, 1971 ), Franklin (Commun Stat Theory Methods 18:489–505, 1989 ), and Singh et al. (Aust NZ J Stat 40:291–297 1998 ) are here considered as data-gathering tools. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Lucio Barabesi & Giancarlo Diana & Pier Perri, 2013. "Design-based distribution function estimation for stigmatized populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 919-935, October.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:7:p:919-935
    DOI: 10.1007/s00184-012-0424-6
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    References listed on IDEAS

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    1. Giancarlo Diana & Pier Perri, 2011. "A class of estimators for quantitative sensitive data," Statistical Papers, Springer, vol. 52(3), pages 633-650, August.
    2. Raghunath Arnab & Sarjinder Singh, 2002. "Estimation of the Size and Mean Value of a Stigmatized Characteristic of a Hidden Gang in a Finite Population: A Unified Approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 659-666, September.
    3. Lucio Barabesi & Marzia Marcheselli, 2010. "Bayesian estimation of proportion and sensitivity level in randomized response procedures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 75-88, July.
    4. Tasos Christofides, 2005. "Randomized response technique for two sensitive characteristics at the same time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 53-63, September.
    5. Lucio Barabesi & Sara Franceschi & Marzia Marcheselli, 2012. "A randomized response procedure for multiple-sensitive questions," Statistical Papers, Springer, vol. 53(3), pages 703-718, August.
    6. Marzia Marcheselli & Lucio Barabesi, 2006. "A generalization of Huang's randomized response procedure for the estimation of population proportion and sensitivity level," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 145-159.
    7. Giancarlo Diana & Pier Francesco Perri, 2010. "New scrambled response models for estimating the mean of a sensitive quantitative character," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1875-1890.
    8. Amitava Saha, 2007. "A simple randomized response technique in complex surveys," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 59-66.
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    Cited by:

    1. Shu-Ching Su & Stephen A. Sedory & Sarjinder Singh, 2015. "Kuk’s Model Adjusted for Protection and Efficiency," Sociological Methods & Research, , vol. 44(3), pages 534-551, August.
    2. Lucio Barabesi & Giancarlo Diana & Pier Perri, 2015. "Gini index estimation in randomized response surveys," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 45-62, January.
    3. Pier Francesco Perri & Elvira Pelle & Manuela Stranges, 2016. "Estimating Induced Abortion and Foreign Irregular Presence Using the Randomized Response Crossed Model," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 601-618, November.
    4. María del Mar Rueda & Beatriz Cobo & Antonio Arcos, 2021. "Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables," Mathematics, MDPI, vol. 9(6), pages 1-13, March.

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