Abstract

This study deals with the extension of the Binary Optional Unrelated Question Model of Sihm et al. (2016) into a stratified set up wherein the prevalence of sensitive characteristic is rare. The Bayes estimator of the sensitivity level is obtained using Beta prior and Squared Error Loss Function. Also, the Bayes estimator of the prevalence of rare sensitive attribute is obtained using a class of non-gamma priors and Linex Loss Function. The corresponding minimal values of Bayes posterior expected loss (BPEL) are also derived. Relative losses are also examined to compare the Bayes estimates with those of the classical estimates. The robustness of the Bayes estimator of the prevalence of rare sensitive attribute is studied with respect to a moderately non-gamma prior distribution and for a class of Linex Loss Function via a numerical illustration.

Author: Samridhi Mehta, Priyanka Aggarwal

Received on: August, 2023

Accepted on: December, 2024