A two-step approach to ratio and regression estimation of finite population mean using optional randomized response models

Year 2016, Volume: 45 Issue: 6, 1819 - 1830, 01.12.2016

Geeta Kalucha Sat Gupta Javid Shabbir

Abstract

We propose a modied two-step approach for estimating the mean of a
sensitive variable using an additive optional RRT model which allows
respondents the option of answering a quantitative sensitive question
directly without using the additive scrambling if they find the question non-sensitive. This situation has been handled before in Gupta et
al. (2010) using the split sample approach. In this work we avoid the
split sample approach which requires larger total sample size. Instead,
we estimate the finite population mean by using an Optional Additive Scrambling RRT Model but the corresponding sensitivity level is
estimated from the same sample by using the traditional Binary Unrelated Question RRT Model of Greenberg et al. (1969). The initial
mean estimation is further improved by utilizing information from a
non-sensitive auxiliary variable by way of ratio and regression estimators. 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.

Keywords

Auxiliary Information, Mean square error, Optional randomized response technique, Ratio estimator, Regression estimator, Unrelated Question RRT Model

References

• . . .