THE LOGISTIC GENERALIZED REGRESSION ESTIMATOR WITH RANDOMIZED RESPONSE SAMPLING WITHOUT REPLACEMENT IN FINITE POPULATIONS: A UNIFYING APPROACH

Abstract

The randomized response technique (RM) introduced by Warner (1965) was designed to avoid non-answers to questions about
sensitive issues and protect the privacy of the interviewee. In this paper, a model assisted survey sampling approach is used to
propose an estimator of the total of individuals with some sensitive characteristic; i.e., we use an auxiliar variable (Fuller and
Park, et al., 2006) in a logistic regression model to improve the estimator. We also propose a model (the G model) that unifies
several other RM approaches under the finite population sampling scheme and the estimators (Särndal, et al., 1992;
Cassel, et al., 1976) framework. We also propose an estimator for the variance of the estimator