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

Issue title: Warner's Randomized Response Model

Guest editors: Arijit Chaudhuri

Article type: Research Article

Authors: Son, Chang Kyoon^a | Kim, Jong Min^{b; *}

Affiliations: [a] Department of Applied Statistics, Dongguk University-Gyeongju, Gyeongju, Gyeongbuk, Korea | [b] Statistics Discipline, Division of Science and Mathematics, University of Minnesota-Morris, Morris, MN, USA

Correspondence: [*] Corresponding author: Jong Min Kim, Statistics Discipline, Division of Science and Mathematics, University of Minnesota-Morris, Morris, MN 56267, USA. E-mail:[email protected]

Abstract: 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.

Keywords: Bayes linear estimator, two-stage randomized response model, stratified randomized response model, optimal sampling design

DOI: 10.3233/MAS-150336

Journal: Model Assisted Statistics and Applications, vol. 10, no. 4, pp. 321-333, 2015