Affiliations: Department of Applied Statistics, Johannes Kepler University Linz, Altenberger Str. 69, Science Park 2, A-4040 Linz, Austria. E-mail: [email protected]
Abstract: Nonresponse and untruthful answers cause serious problems in sample and population surveys on sensitive variables. In this article, firstly, the idea of Liu and Chow  for the estimation of relative sizes of different categories applicable in the field of opinion polls is explicated for complex sampling designs. Secondly, in the case that the moment estimator lies outside the parameter space a Maximum Likelihood solution is presented along with a method to allow the calculation of confidence intervals. Thirdly, the privacy protection offered by the method is discussed. A concluding simulation study allows a look on the effect of the usage of this questioning design from different aspects.