Bayesian Estimation Using Warner's Randomized Response Model through Simple and Mixture Prior Distributions

摘要

Bayesian estimation of population proportion of a sensitive characteristic is proposed by adopting a simple beta distribution and a mixture of Beta distributions as quantification of prior information using simple random sampling with replacement. In the sequel application of the stratified random sampling is also studied in Bayesian scenario. It is assumed that data are collected through Warner (196524. Warner , S. L. ( 1965 ). Randomized response: a survey technique for eliminating evasive answer bias . Journal of the American Statistical Association 60 : 63 - 69 . [Taylor & Francis Online], [PubMed], [Web of Science ®]View all references) randomized response technique. To study the performance of Bayesian estimators we have used Mean Squared Error (MSE) and/or Relative Efficiency (RE) as performance criterion. Further, comparison of the suggested estimator is made with Kim et al. (200612. Kim , J. M. , Tebbs , J. M. , An. S. W. ( 2006 ). Extensions of Mangat's randomized response model . Journal of Statistical Planning & Inference 36 ( 4 ): 1554 - 1567 . [CrossRef]View all references) stratified estimator and usual maximum likelihood estimator in case of stratified random sampling. It is observed that unlike the moment and maximum likelihood methods, proposed Bayesian estimation method is free of the problems of having an estimate of population proportion outside the interval (0, 1) and large variance when the sample proportion of yes responses is very low or very high.