Mean square error estimation in randomized response surveys

Abstract

Warner [10] pioneered the randomized response (RR) technique for collecting information on a sensitive qualitative characteristic. Following Rao [7] and Chaudhuri and Stenger [6] an attempt has been made to derive an exact expression for the mean square error of ratio estimator, regression estimator, separate and combined ratio estimator, separate and combined regression estimator in stratified random sampling and the generalized regression estimator in case of randomized response surveys dealing with a sensitive quantitative character, for example, expenditure on drinking alcohol, additional income earned over usual salary to hide income tax in the income tax return, expenditure on gambling, number of induced abortions, income earned through prostitution, expenditure incurred towards payment of prostitutes in a red light area and some such others which we do not want to disclose even to our wives. Also an exact expression for an unbiased estimator of the mean square error of each of the above estimators is worked out.