Abstract
This article is about studying ratio, product and regression methods for estimating sensitive mean using a two-stage optional randomized response model by Gupta et al. (2010) and information on non-sensitive auxiliary variable. In particular, the additive randomized response model is used to further enhance the efficiency of the ratio, product and regression estimators (Gupta et al., 2010). We compare our proposed auxiliary information based two-stage optional randomized response estimator with recently proposed auxiliary information-based estimators. Through algebraic comparisons, it is shown that the proposed ratio, product and regression estimators are better than the corresponding estimators proposed in some recent studies. The results are also supported by a numerical study.
Highlights
Since long, the sample survey has been appreciated as a go to method for the procurement of data from several areas of human interest
Some of the survey practitioners have noted troublesome points about the negative effect of social desirability bias (SDB) on the correctness of results obtained through surveys
Some of them are noted here as Heijden et al (2000) observed that 75% of the respondents who had committed welfare or unemployment benefit fraud denied having done so in faceto-face interviews; Lee and Sargeant (2011) noted that 65% of the respondents over-reported their donations; Stecklov et al (2015), observed that high reported use of sterilization is correlated with propensity of respondents to present themselves in a positive way in front of interviewers
Summary
The sample survey has been appreciated as a go to method for the procurement of data from several areas of human interest. The most effective approach to deal with the problem of SDB is the randomized response techniques (RRT), initially, presented by Warner (1965). Motivated by the successful applications of auxiliary information in sensitive surveys, we intend to make use of auxiliary information along with a two-stage optional randomized response model of Gupta et al (2010) to suggest ratio, product and regression estimators. The intended ratio, product and regression estimators are based on one non-sensitive auxiliary variable.
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