Estimation of the mean of a socially undesirable characteristic

This paper focuses on presenting a generalization of the scrambled response models of Hussain and 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 randomized response model: estimation of mean”, Journal of Applied Statistics, 36(12), pp. 1361–1367 (2009)]. The suggested generalization is helpful in procuring honest data on socially undesirable characteristics. The suggested estimator is found to be unconditionally more efficient in terms of variablity. From a privacy point of view, comparison of the proposed class of models is made using the privacy protection measure by Zaizai et al. [Zaizai, Y., Jingu, W. and Junfeng, L. “An efficiency and protection based comparison among the quantitative randomized response strategies”, Communications in Statistics-Theory and Methods, 38, pp. 400–408 (2009)]. Unlike many scrambled response models, the proposed class of models is free from the need of known parameters of scrambling variables. The relative numerical efficiency of the proposed model is simulated for some fixed values of the parameters. The practical application of the proposed model is also studied through a small scale survey.