Estimating Sensitive Proportions from Randomized Responses in Unequal Probability Sampling

Abstract

Warner (1965) introduced the technique of randomized response (RR) surveys in unbiasedly estimating the proportion of individuals in a community bearing a sensitive characteristic with an aim at protection of privacy. Many researchers developed alternative devices inducing refinements thereupon and posing modified problems of diverse peculiarities of interest. In each case dealing with qualitative characteristics the published literature permits sample selection only with equal probabilities ‘with’ replacement and as rare exception ‘without’ replacement. Three works by Chaudhuri (1999, 2001 a, b) alone illustrate application of uneuqal probability sampling without replacement to take specific care of some of these problems of attribute estimation. Here a few more such cases are covered with appropriately revised devices.