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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We propose a modified two-step approach for estimating the mean of a sensitive variable using an additive optional RRT model which allows respondents the option of answering a quantitative sensitive question directly without using the additive scrambling if they find the question non-sensitive. This situation has been handled before in using the split sample approach. In this work we avoid the split sample approach which requires larger total sample size. Instead, we estimate the finite population mean by using an Optional Additive Scrambling RRT Model but the corresponding sensitivity level is estimated from the same sample by using the traditional Binary Unrelated Question RRT Model of Greenberg et al. (1969). The initial mean estimation is further improved by utilizing information from a non-sensitive auxiliary variable by way of ratio and regression estimators. 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.