Applied Mathematics and Information Sciences

Abstract

The methodology of randomized response has advanced considerably in recent years. Nevertheless, to date all the proposed estimators with randomized response techniques have been based on the hypothesis of the availability of a unique and complete list of units forming the target population to be used as a sampling frame. In this paper, we present a new procedure aimed at determining a population total using a model of randomized response when data are obtained from two frames. We introduce different ways of combining estimates obtained from the different frames and propose unbiased estimators, with an analytic expression for their variances. Estimates for the variances are also obtained, applying analytical formulas such as those based on resampling technologies. A simulation study illustrates the behaviour of the estimator using diverse randomization devices.