Warner in practice: How to incorporate true answers in a generalized Warner model

Abstract

Untruthful answers and nonresponse might cause serious problems in sample and population surveys on sensitive variables. In honor of the 50 year jubilee of Warner's basic idea in the field of randomized response techniques, this particular strategy is extended to general probability sampling with arbitrary sample inclusion probabilities. The statistical properties of the derived estimator for the relative size of an interesting subpopulation are presented in the context of data imputation. Moreover, the theory is extended to the realistic case that some of the respondents might be willing to answer on the direct question. The effect of a certain behavior of the interviewees on the statistical properties of the estimator is discussed.