Abstract
This article considers unbiased estimation of mean, variance and sensitivity level of a sensitive variable via scrambled response modeling. In particular, we focus on estimation of the mean. The idea of using additive and subtractive scrambling has been suggested under a recent scrambled response model. Whether it is estimation of mean, variance or sensitivity level, the proposed scheme of estimation is shown relatively more efficient than that recent model. As far as the estimation of mean is concerned, the proposed estimators perform relatively better than the estimators based on recent additive scrambling models. Relative efficiency comparisons are also made in order to highlight the performance of proposed estimators under suggested scrambling technique.
Highlights
To procure reliable data on stigmatizing characteristics, Warner [1] introduced the notion of randomized response technique where the respondent himself selects randomly one of the two complementary questions on probability basis
We show that there is no need of large value of the parameter (T or F) when the study variable is either low, moderately or highly sensitive
He/she reports true value of study variable both the times. This is not challenging since the respondents feeling study variable insensitive would be willing to dispose their true value on sensitive variable
Summary
To procure reliable data on stigmatizing characteristics, Warner [1] introduced the notion of randomized response technique where the respondent himself selects randomly one of the two complementary questions on probability basis. As far as estimation of mean is concerned, we show that the proposed ORRM is better than Mehta et al [14], Huang [12] and Gupta et al [13] ORRMs. We show that there is no need of large value of the parameter (T or F) when the study variable is either low, moderately or highly sensitive. Let Z’ij be the optional scrambled response from jth respondent in the ith subsample taking F~0 in (1)–(5), unbiased estimators and their variances are given by: m^XG ~. Let mSi ~1, be the known mean, and s2Si ~c2i , be the known variance of the positive-valued random variables Si. The optional randomized response Zi’j’ from jth respondent in the ith subsample is given by: Zi’j’~ 1{ Yj XjzYj SijXjzDij , ð11Þ. ÁÉ : applying Theorem 2.3, we get: EÈV^ arðY ÞÉ~EÀW^ ZÁ{EÀW^ Z2 ÁzVarÀW^ ZÁ
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