An Improved Exponential Type Estimator Of Population Mean of Sensitive Variable Using Optional Randomized Response Technique

Lovleen Kumar Grover,Amanpreet Kaur

doi:10.18187/pjsor.v15i1.2588

Abstract

In this paper, we improve the efficiency of Koyuncu et al (2014)’s estimator of population mean of sensitive variable by replacing Traditional Randomized response technique with Optional Randomized response technique as suggested by Gupta et al (2014). The mean square error of proposed estimator is obtained, up to first order of approximation, and is compared with mean square error of various existing estimators theoretically as well as numerically.

Highlights

We know that auxiliary information plays an important role to improve the efficiency of an estimator of parameter of interest when the study variable is sensitive or non-sensitive in nature
Bahl and Tuteja (1991), Grover and Kaur (2011), Singh and Solanki (2012) and many more authors used auxiliary information when the study variable is non sensitive whereas Sousa et al (2010), Gupta et al (2012), Koyuncu et al (2014), Kalucha et al (2015) and many more authors used auxiliary information in Randomized response technique (RRT) under traditional additive model when the study variable is sensitive
In an Optional RRT Model, scrambled answer is given by the respondent only if he/she consider the question is sensitive otherwise true answer is given by the respondent

Summary

Introduction

We know that auxiliary information plays an important role to improve the efficiency of an estimator of parameter of interest when the study variable is sensitive or non-sensitive in nature. Bahl and Tuteja (1991), Grover and Kaur (2011), Singh and Solanki (2012) and many more authors used auxiliary information when the study variable is non sensitive whereas Sousa et al (2010), Gupta et al (2012), Koyuncu et al (2014), Kalucha et al (2015) and many more authors used auxiliary information in Randomized response technique (RRT) under traditional additive model when the study variable is sensitive. Gupta et al (2014) suggested an efficient estimator of population mean of sensitive variable by replacing traditional RRT model used in Sousa et al (2010) and Gupta et al (2012) with Optional RRT model. To support theoretical results obtained, a numerical illustration is considered

Notations and existing estimators

Proposed exponential estimator and its properties

Comparison of the proposed estimator with the existing estimators

Numerical illustration

Conclusion