Abstract
This paper considers the concomitant-based rank set sampling (CRSS) for estimation of the sensitive proportion. It is shown that CRSS procedure provides an unbiased estimator of the population sensitive proportion, and it is always more precise than corresponding sample sensitive proportion (Warner SL (1965)) that based on simple random sampling (SRS) without increasing sampling cost. Additionally, a new estimator based on ratio method is introduced using CRSS protocol, preserving the respondent’s confidentiality through a randomizing device. The numerical results of these estimators are obtained by using numerical integration technique. An application to real data is also given to support the methods.
Highlights
In some social surveys, we may encounter the problem of estimating the proportion of the population having sensitive attribute, such as drug addicts, users of heron and non-taxpayers, for which people are not inclined to respond truthfully
As the interviewer is kept unaware of the result produced by the said device, the use of this technique ensures that the respondent cannot be recognized on the basis of his/her response
After development of the first randomized response model [1], numerous variants have been suggested by different researchers to obtain more reliable estimates of the sensitive attribute by increasing respondent’s degree of privacy
Summary
We may encounter the problem of estimating the proportion of the population having sensitive attribute, such as drug addicts, users of heron and non-taxpayers, for which people are not inclined to respond truthfully. In such situations the techniques for collecting direct information may result in elusive, ambiguous, and even no response. [18] has adopted model-based ranking approach, introduced by [17], for studying sensitive proportion using concomitant based-rank set sampling This ranking method requires estimated success probabilities by fitting the logistic regression. A new estimator based on ratio method is introduced under CRSS plan
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