Ratio estimation of the mean under RRT models

Abstract

Ratio estimation is a parameter estimation technique that uses a known auxiliary variable that is correlated with the study variable. In many situations, the primary variable of interest may be sensitive and it cannot be observed directly. However, we can observe directly a non-sensitive variable that is highly correlated with the study variable. In these cases, we have to rely on some Randomized Response Technique (RRT) models to obtain information on the study variable.In this thesis, we rst review some RRT models, some general ratio and product estimation techniques, and two Kalucha et al. (2015) ratio estimators that are based on Gupta et al. (2010) additive optional RRT model. One of the Kalucha et al. (2015) estimators, the multiplicative ratio estimator, did not work eciently and was abandoned. The main focus of this thesis is on xing the Kalucha et al. (2015)abandoned multiplicative ratio estimator and reevaluating its performance. We discuss the Bias and the Mean Square Error (MSE) of our proposed multiplicative ratio estimator correct up to rst order approximation, and present the comparisons with other estimators under the additive optional RRT model. A simulation study is also conducted to verify the theoretical result. 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).

Median estimation in the presence of non-response using randomised response technique

“…The results obtained showed a better efficiency of the estimator. Zhang et al (2019) presented a geometric mean proportion assessor for the limited population mean utilizing discretionary RRT models. The outcomes showed that the mean of the mathematics assessor is more effective than the standard mean RRT mean assessment in circumstances where the linkage with coefficient among the variables of review and the assistant is higher than 0.5.…”

Using ORRT Models for Mean Estimation under Nonresponse and Measurement Errors in Stratified Successive Sampling

“…Furthermore, it is extended by the work of Diana and Perri [8] who proposed a class of estimators for quantitatively sensitive data. Likewise, Gupta et al [9] suggested a unifed measure of respondent privacy and model efciency in quantitative RRT models; Zhang et al [10] proposed a ratio estimation of the mean under RRT models and many others. Nonresponse and measurement errors may be observed in a socioeconomic survey on sensitive data.…”

Estimation of Sensitive Variable in Two-Phase Sampling under Measurement Error And Non-Response Using ORRT Models

“…So, Gupta et al (2002) modified Eichhorn and Hayre's (1983) multiplicative scrambling RRT model and developed an Optional randomized response technique (ORRT), which allows researchers to estimate not only the mean of the variable of interest, but also the sensitivity level P . Furthermore, Gupta et al (2014; 2018; 2012, Zhang et al (2018), Mushtaq and Amin (2020) etc have worked on estimation of mean of sensitive variable using ORRT.…”