Bayesian Analysis of Warner’s Randomized Response Technique

Abstract

This paper proposed alternative beta estimators of the population proportion of a sensitive attribute when life data were obtained through the administration of survey questionnaires on abortion of some matured women. The results showed that the proposed alternative beta estimators were more efficient in capturing responses from respondents than the simple beta estimator proposed by Winkler and Franklin for relatively small, medium as well as large sample sizes respectively.

Bayesian Estimation ofWarner’s Randomized Response Technique with Transmuted Kumaraswamy Prior

“…The primary focus of this paper is to propose Bayesian estimation of Warner's randomized response technique of a population proportion of respondents possessing a sensitive attribute using transmuted Kumaraswamy prior. This study complements the work of Winkler and Franklin (1979), Spurrier and Padgett (1980), Pitz (1980), Migon, H. and Tachibana (1997), Bar-Lev et al (2003), Kim et al (2006), Barabesi and Marcheselli (2006), Hussain and Shabbir (2009), Hussain et al (2011), Hussain and Shabbir (2012), Hussain et al (2014), Adewara 2017, Adepetun andAdewara 2018), Narjis and Shabbir (2021a), Ahmed et al (2021) in the Bayesian frameworks. The rest of the paper is arranged as follows.…”

“…where f = 1−p 2p−1 for p = 0.5. The mean square error of πSW is Adepetun and Adewara (2017) proposed Bayes estimator using distribution proposed by Kumaraswamy (1980) as their alternative prior which was defined as:…”

“…The study adopted benchmark data obtained by administering survey questionnaires on abortion and use of contraceptives by some women in Akure metropolis, Nigeria (Adepetun and Adewara 2017). A total of 300 questionnaires were administered with 279 returned.…”

New Stratified Bayesian Estimators Using Warner’s Randomized Response Technique Through Mixed Priors

“…Although there is enormous work on the Bayesian inference, in general the work on Bayesian analysis of randomized response techniques is limited. Researches that have been carried out on the Bayesian analysis of randomized response techniques include Bar-Lev et al [13], Migon and Tachibana [14], Oh [15], O'Hagan [16], Pitz [17], Unnikrishnan and Kunte [18], Winkler and Franklin [19], Adepetun and Adewara [20][21][22][23].…”