Generalized Scrambling in Quantitative Optional Randomized Response Models

Gupta, Sat; Mehta, Samridhi; Shabbir, Javid; Dass, Bal Kishan

doi:10.1080/03610926.2011.638427

Cited by 22 publications

(8 citation statements)

References 10 publications

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“…The basic premise behind ORR models is that a question may be sensitive for one respondent but may not be sensitive for another respondent. ORR models have also been studied by Huang (2010) and Gupta et al (2013).…”

Section: Introductionmentioning

confidence: 98%

Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

Kalucha

Gupta

Dass

2015

Journal of Statistical Theory and Practice

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Auxiliary information is commonly used in sample surveys in order to achieve higher precision in the estimates. In this article we are concerned with the utilization of auxiliary information in the estimation stage in simple random sampling without replacement (SRSWOR), making use of an optional randomized response model proposed by Gupta et al. (2010). The underlying assumption is that the primary variable is sensitive in nature but a nonsensitive auxiliary variable exists that is positively correlated with the primary variable. We propose a ratio estimator of finite population mean and call it the additive ratio estimator. Expressions for the bias and mean square error of the proposed estimator are obtained to first order of approximation. Efficiency comparisons with the ordinary optional randomized response technique (RRT) mean estimator of Gupta et al. (2010) are carried out both theoretically and numerically. A simulation study is presented to evaluate the performance of the proposed estimator.

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Section: Introductionmentioning

confidence: 98%

Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

Kalucha

Gupta

Dass

2015

Journal of Statistical Theory and Practice

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“…The Gupta et al (2006) one-stage optional RRT model and the Gupta et al (2010) two-stage optional RRT model were both based on additive scrambling that eliminated the need for any approximation by using a split-sample approach. The role of multiplicative scrambling is further questioned in Gupta et al (2012), where it was observed that the additive scrambling performs better than the linear combination scrambling of Huang (2010). Keeping in mind this background, we use additive scrambling in the current work.…”

Section: Introductionmentioning

confidence: 87%

A Three-Stage Optional Randomized Response Model

Mehta

Dass

Shabbir

et al. 2012

Journal of Statistical Theory and Practice

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In Gupta et al. (2010;2011), it was observed that introduction of a truth element in an optional randomized response model can improve the efficiency of the mean estimator. However, a large value of the truth parameter (T) may be needed if the underlying question is highly sensitive. This can jeopardize respondent cooperation. In what we call a "three-stage optional randomized response model," a known proportion (T) of the respondents is asked to tell the truth, another known proportion (F) of the respondents is asked to provide a scrambled response, and the remaining respondents are instructed to provide a response following the usual optional randomized response strategy where a respondent provides a truthful response (or a scrambled response) depending on whether he/she considers the question nonsensitive (or sensitive). This is done anonymously based on color-coded cards that the researcher cannot see. In this article we show that a three-stage model may turn out to be more efficient than the corresponding two-stage model, and with a smaller value of T. Greater respondent cooperation will be an added advantage of the three-stage model.

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“…But auxiliary variable is non sensitive in both the situations. Some authors including Gupta et al (2010), Huang (2010), Gupta et al (2013), and Gupta et al (2014) have studied Optional RRT with modified additive model. Tarray and Singh (2017) have suggested optional RRT with new additive model.…”

Section: Introductionmentioning

confidence: 99%

An Improved Exponential Type Estimator Of Population Mean of Sensitive Variable Using Optional Randomized Response Technique

Grover

Kaur

2019

Pak.j.stat.oper.res.

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In this paper, we improve the efficiency of Koyuncu et al (2014)’s estimator of population mean of sensitive variable by replacing Traditional Randomized response technique with Optional Randomized response technique as suggested by Gupta et al (2014). The mean square error of proposed estimator is obtained, up to first order of approximation, and is compared with mean square error of various existing estimators theoretically as well as numerically.

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Generalized Scrambling in Quantitative Optional Randomized Response Models

Cited by 22 publications

References 10 publications

Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

A Three-Stage Optional Randomized Response Model

An Improved Exponential Type Estimator Of Population Mean of Sensitive Variable Using Optional Randomized Response Technique

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