Ratio estimation of the mean under RRT models

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Qi Zhang (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Sat Gupta

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 first 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 efficiently and was abandoned. The main focus of this thesis is on fixing 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 first 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 efficient 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).

Additional Information

Language: English
Date: 2016
Ratio Estimator, RRT
Estimation theory
Sampling (Statistics)

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