Affiliations: Interdisciplinary Statistical Recearch Unit, Indian Statistical Institute, Kolkata, West Bengal, India. E-mail: [email protected]
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.
Keywords: Generalized regression estimator, mean square error, ratio estimator, regression estimator, separate and combined ratio estimator, separate and combined regression estimator
