Estimating a distribution for each category of a sensitive variate

The use of a Randomized Response (RR) design makes it possible to estimate the distribution of a sensitive variate. In this paper, the estimation of the distribution of a non-sensitive variate for each category of a sensitive variate is considered for the case where data on the sensitive variate is obtained by use of an RR procedure. Simple estimators are developed without making any distributional assumptions about the non-sensitive variate. However, if distributional assumptions are made, it is shown that the EM algorithm may be used to compute Maximum Likelihood estimates. Computational comparisons of the estimators, using simulation, indicate that the simple estimators perform well, particularly for large sample sizes.