Abstract

HUSSAIN, ZAWAR; ALI SHAH, EJAZ; SHABBIR, JAVID  and  RIAZ, MUHAMMAD. On an Improved Bayesian Item Count Technique Using Different Priors. Rev.Colomb.Estad. [online]. 2013, vol.36, n.2, pp.303-317. ISSN 0120-1751.

Item Count Technique (ICT) serves the purpose of estimating the proportion of the people with stigmatizing attributes using the indirect questioning method. An improved ICT has been recently proposed in the literature (not requiring two subsamples and hence free from finding optimum subsample sizes unlike the usual ICT) in a classical framework that performs better than the usual ICT and the Warner method of Randomized Response (RR) technique. This study extends the scope of this recently proposed ICT in a Bayesian framework using different priors in order to derive posterior distributions, posterior means and posterior variances. The posterior means and variances are compared in order to study which prior is more helpful in updating the item count technique. Moreover, we have compared the Proposed Bayesian estimation with Maximum Likelihood (ML) estimation. We have observed that simple and elicited Beta priors are superior choices (in terms of minimum variance), depending on the sample size, number of items and the sum of responses. Also, the Bayesian estimation provides relatively more precise estimators than the ML Estimation.

Keywords : Bayesian Estimation; Indirect Questioning; Item Count Technique; Population Proportion; Prior Information; Privacy Protection; Randomized Response Technique; Sensitive Attributes.

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