Mean and sensitivity estimation in optional randomized response models

Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

“…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.…”

“…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.…”

A two-step approach to ratio and regression estimation ofnite population mean using optional randomized response models

“…Expressions for the Bias and MSE of the proposed estimators (correct up to first order approximation) are derived. We compare the results of this new model with those of the split-sample based Optional Additive RRT Model of Kalucha et al (2015), Gupta et al (2015) and the simple optional additive RRT Model of Gupta et al (2010). We see that the regression estimator for the new model has the smallest MSE among all of the estimators considered here when they have the same sample size.…”

“…Choice of scrambling mechanism plays an important role in quantitative response models. Eichhron and Hayre (1983), Gupta and Shabbir (2004), Gupta et al (2002Gupta et al ( , 2010, Wu et al (2008) and many others have estimated the mean of a sensitive variable when the study variable is sensitive and no auxiliary information is available. While Eichhron and Hayre (1983) have used multiplicative scrambling, Gupta et al (2010) have used additive scrambling in the context of optional randomized response models where a respondent provides a true response if he/she considers the question non-sensitive, and provides a scrambled response if the question is deemed sensitive.…”

Generalized Family of Estimators for Imputing Scrambled Responses

“…A randomized device was used to collect the responses from the respondents and protected their privacy despite of getting direct response. After Warner, various randomized response models were used for estimating the proportion of the nominal variable in the population(see e.g., Greenberg et al (1969), Folsom et al (1973), Mangat and Singh (1990), Gupta et al (2010)). Greenberg et al (1971), Eichhorn and Hayre (1983), Mangat and Singh (1990), Gupta et al (2013) considered the simple and multistage scrambling models (MSM) for estimating the mean of sensitive variables.…”