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.

Ratio estimation of the mean under RRT models

“…Both the theoretical and the empirical results show that the proposed multiplicative ratio estimator is more ecient than the ordinary RRT estimator that does not utilize the auxiliary variable. It also compares well with the additive ratio estimator of Kalucha et al (2015).…”

“…In addition, ratio and product estimators provide more accurate results than the ordinary mean estimator when an auxiliary variable that is highly correlated with the study variable is used. These two estimators have been used by many researchers [15] proposed two ratio estimators in the context of optional RRT models. They showed that one of them, the additive ratio estimator, is more ecient than the estimator by [13].…”

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.…”

“…The tables below provide a comparison between the proposed model and the split-sample additive scrambling models of Kalucha et al (2015) and Gupta et al (2015) in the presence of non-sensitive auxiliary information. We choose the parameters as per the observation A1 (given below) that was obtained in Gupta et al (2015) under which the regression estimatorμ Areg is more efficient than both additive ratio estimatorμ AR and the ordinary mean estimatorμ Y under the split sample approach: A1.…”

“…Sousa et al (2010) and Gupta et al (2012) suggested mean estimators based on full additive RRT models using an auxiliary variable. Kalucha et al (2015) and Gupta et al (2015) improved the mean estimators further by using optional additive RRT models which apart from estimating µ Y (the mean of sensitive variable Y ) also estimated W (the sensitivity level of the research question) using a split-sample approach. Recently Singh and Tarray (2014) have studied optional randomized response model in the stratified sampling setting.…”