Bayes linear estimator for two-stage and stratified randomized response models

Chang Kyoon Son, Jong-Min Kim

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, we suggest the Bayes linear estimator (BLE) for randomized response model (RRM) to improve the efficiency of RR estimators, only using the first and second prior moments. The randomized response model is an indirect questioning technique used to protect the privacy of respondents in a survey regarding a sensitive characteristic. Meanwhile Bayes linear estimation is useful for parameter estimation compared to the typical Bayesian method because it only uses the first and second prior knowledge of the variable of interest. Also, it has an advantage of robustness with the distribution. We suggest the Bayes linear estimators for the two-stage and the stratified RRM and find the optimal sample size to minimize the Bayes risk for the stratified RRM. Also, we show the difference in efficiency between the Bayes linear estimators and the typical non-Bayesian RR estimators by simulation study.

Original languageEnglish (US)
Pages (from-to)321-333
Number of pages13
JournalModel Assisted Statistics and Applications
Issue number4
StatePublished - Nov 16 2015


  • Bayes linear estimator
  • optimal sampling design
  • stratified randomized response model
  • two-stage randomized response model


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