Risk-optimal estimators for survey procedures with certain indirect questions

Abstract

Surveys usually consist of a list of direct questions. However respondents reluctantly provide direct information on sensitive topics such as socially undesired behavior (e.g., social fraud, discrimination, tax evasion), income or political preferences. For this reason, the diagonal technique (DT), an indirect questioning procedure has been proposed in the literature. In this paper, we consider multiple categorical target variables where all or some of the variables are gathered by the DT. The maximum likelihood (ML) estimator for the joint distribution depends on the setup of the survey procedure, i.e., on certain parameters to adjust. We conduct a decision-theoretic analysis and derive risk-optimal ML estimators. The special point of our investigation is the incorporation of the degree of privacy protection (DPP). In particular, in the class of ML estimators corresponding to a given DPP, we detect an estimator with the lowest risk, i.e., with the highest quality.