Estimation of the mean of a socially undesirable characteristic

This paper focuses on presenting a generalization of the scrambled response models of hussainand shabbir [hussain, z. and shabbir, j. ``on estimation of mean of a sensitive quantitative variable'',interstat, (#006), (2007)] and gjestvang and singh [gjestvang, c.r. and singh, s. ``an improved randomizedresponse model: estimation of mean'', journal of applied statistics, 36(12), pp. 13611367 (2009)]. thesuggested generalization is helpful in procuring honest data on socially undesirable characteristics. thesuggested estimator is found to be unconditionally more efficient in terms of variablity. from a privacypoint of view, comparison of the proposed class of models is made using the privacy protection measureby zaizai et al. [zaizai, y., jingu, w. and junfeng, l. ``an efficiency and protection based comparison amongthe quantitative randomized response strategies'', communications in statistics-theory and methods, 38,pp. 400408 (2009)]. unlike many scrambled response models, the proposed class of models is free fromthe need of known parameters of scrambling variables. the relative numerical efficiency of the proposedmodel is simulated for some fixed values of the parameters. the practical application of the proposedmodel is also studied through a small scale survey.