Estimation of Mean of a Sensitive Quantitative Variable in Complex Survey: Improved Estimator and Scrambled Randomized Response Model

Abstract

With the intention to control a true swapping between the efficiency and the privacy protectionthis paper introduces a scrambled randomized response (SRR) model to be alternative of Saha’sscrambling mechanism. The basic initiative is to provide an assortment of the additive, thesubtractive and the multiplicative models. The simulation and the empirical studies are providedfor various sample sizes to compare the efficiency of the proposed model. The results obtainedfrom simulation showed that the proposed model performs better than Pollock and Bek’s additivemodel. Also, the proposed generalized estimator of mean has been studied using a new SRRmodel presented in this article and shown that the proposed estimator and its class of estimatorsare more efficient than existing estimators. It is also shown that gain in efficiency is more whenthe proposed SRR model is used. The efficiency of the proposed class of estimators over existingestimators using both models is also provided using real data and with a simulation study.