Abstract
Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.
Similar content being viewed by others
References
Allen J, Singh S (2001) Response techniques to analyse various transformation and selection probabilities. Interstat. Available at http://interstat.statjournals.net/YEAR/2001/abstracts/0111002.php
Bhargava M and Singh R (2000). A modified randomization device for Warner’s model. Statistica LX: 315(-321): 315–321
Chaudhuri A (2004). Christofides’randomized response technique in complex sample survey. Metrika 60: 223–228
Chaudhuri A and Mukerjee R (1988). Randomized response: theory and techniques. Marcel Dekker, Inc., New York
Cochran WG (1977). Sampling techniques. Wiley, New York
Diana G, Perri PF (2007a) Regression type strategy for randomized response. In: Proceedings of the 2007 intermediate conference of the italian statistical society—risk and prediction—venice. 6-8 June, pp 459–460, Cleup, Padova
Diana G and Perri PF (2007). Estimation of finite population mean using multi-auxiliary information. Metron LXV: 99–112
Fox JA and Tracy PE (1986). Randomized response: a method for sensitive survey. Sage Publication, Inc., Newbury Park
Greenberg BG, Abul-Ela ALA, Simmons WR and Horvitz DG (1969). The unrelated question randomized response model: theoretical framework. J Am Stat Assoc 64: 520–539
Grewal IS, Bansal ML and Sidhu SS (2006). Population mean corresponding to Horvitz–Thompson’s estimator for multi-characteristics using randomized response technique. Model Assist Stat Appl 1: 215–220
Hedayat AS and Sinha BK (1991). Design and inference in finite population sampling. Wiley, New York
Horvitz DG, Shah BV, Simmons WR (1967) The unrelated question randomized response model. In: Social statistics section proceedings of the American statistical association, pp 65–72
Huang K-C. (2005). Estimation of sensitive data from a dichotomous population. Stat Pap 47: 149–156
Mangat NS (1994). An improved randomized response strategy. J R Stat Assoc B 56: 93–95
Mangat NS and Singh R (1990). An alternative randomized response procedure. Biometrika 77: 439–442
Mangat NS, Singh S and Singh R (1995). On use of a modified randomization device in Warner’s model. J Indian Soc Stat Oper Res 16: 65–69
Saha A (2006). A generalized two-stage randomized response procedure in complex sample survey. Aust NZ J Stat 48: 429–443
Shabbir J and Gupta S (2005). On modified randomized device of Warner’s model. Pak J Stat 21: 123–129
Singh S (2003). Advanced sampling theory with applications, vol 2. Kluwer, Dordrecht
Singh HP and Mathur N (2002). On Mangat’s improved randomized response strategy. Statistica LXII: 397–403
Singh S, Horn S, Singh R and Mangat NS (2003). On the use of modified randomization device for estimating the prevalence of a sensitive attribute. Stat Transit 6: 515–522
Srivastava SK (1971). A generalized estimator for the mean of a finite population using multi-auxiliary information. J Am Stat Assoc 66: 404–407
Sukhatme PV, Sukhatme BV, Sukhatme S and Asok C (1984). Sampling theory of surveys with applications. Iowa State University Press, Ames
Tracy DS and Mangat NS (1996). On respondet’s jeopardy in two alternative questions randomized response model. J Stat Plan Inference 55: 107–114
Warner SL (1965). Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60: 63–69
Zaizai Y (2006). Ratio method of estimation of population proportion using randomized response technique. Model Assist Stat Appl 1: 125–130
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Diana, G., Perri, P.F. Estimating a sensitive proportion through randomized response procedures based on auxiliary information. Stat Papers 50, 661–672 (2009). https://doi.org/10.1007/s00362-007-0107-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-007-0107-y