The item count technique (ICT) is a helpful tool to conduct surveys on sensitive characteristics such as tax evasion, corruption, insurance fraud, social fraud or drug consumption. The ICT yields cooperation of the respondents by protecting their privacy. There have been several interesting developments on the ICT in recent years. However, some approaches are incomplete while some research questions can not be tackled by the ICT so far. For these reasons, we broaden the existing literature in two main directions. First, we generalize the single sample count (SSC) technique, which is a simplified version of the original ICT, and derive an admissible estimate for the proportion of persons bearing a stigmatizing attribute, bootstrap variance estimates and bootstrap confidence intervals. Moreover, we present both a Bayesian and a covariate extension of the generalized SSC technique. The Bayesian set up allows the incorporation of prior information (e.g., available from a previous study) into the estimation and thus can lead to more efficient estimates. Our covariate extension is useful to conduct regression analysis, i.e., to estimate the effects of explanatory variables on the sensitive characteristic. Second, we establish a new ICT that is applicable to multicategorical sensitive variables such as the number of times a respondent has evaded taxes or the amount of money earned by undeclared work (recorded in classes). The estimation of the distribution of such attributes was not at all treated in the literature on the ICT so far. Therefore, we derive estimates for the marginal distribution of the sensitive characteristic, Bayesian estimates and regression estimates corresponding to our multicategorical ICT.
"Improvements and extensions of the item count technique." Electron. J. Statist. 8 (2) 2321 - 2351, 2014. https://doi.org/10.1214/14-EJS951