Model assisted estimation of sensitive proportions from randomised responses by unequal probability sampling

Article type: Research Article

Authors: Pal, Sanghamitra^{a; *} | Chaudhuri, Arijit^b

Affiliations: [a] Department of Statistics, West Bengal State University, Barasat, India | [b] Applied Statistics Unit, Indian Statistical Institute, Kolkata, India

Correspondence: [*] Corresponding author: Sanghamitra Pal, Department of Statistics, West Bengal State University, Barasat, India. Tel.: +91 9830294972; Fax: +91 33 25241977; E-mail: [email protected].

Abstract: In order to estimate the proportion of people bearing a sensitive characteristic in a community, a sample is selected with unequal probabilities and randomized response data are obtained. Supposing data on a related variable are at hand in addition a model-design based estimation procedure modifying Chaudhuri and Saha’s (2004) is developed and studied. Four well-known Randomized Response (RR) methods are illustrated and a one-parameter logistic regression model is tried. Empirical Bayes estimation is examined and simulated results are presented to study the resulting efficacy.

Keywords: Empirical Bayes, one parameter logistic, qualitative characteristic, stigmatizing features, Warner’s and other RR models AMS Subject Classification: 62 DO5

DOI: 10.3233/MAS-170417

Journal: Model Assisted Statistics and Applications, vol. 13, no. 1, pp. 53-61, 2018