Quantitative Issues Bearing Stigma: Parameter Estimation

Abstract

A brief outline of the general theory of estimating finite population totals and means based on a sample selected with a suitable sampling design is given. Initially it is assumed that direct responses are available and then the theory is developed in the case when the sensitivity of the data on the quantitative characteristic makes it necessary to implement suitable devices to collect randomized response data. Two different randomized response devices are considered. The theory of estimation is illustrated in case the sample is selected employing the Rao-Hartley-Cochran sampling scheme as well as in the case of a general sampling scheme and when the data are collected using either of the two devices. Techniques which allow for direct responses by participants are presented. Such approaches are based on the idea that some people may consider the item in question not sensitive enough and therefore both options for providing a direct response or a randomized one are available. The main advantage of these optional randomized response techniques is the variance reduction of the produced estimators.