Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

Abstract

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.