Estimation of finite population distribution function of sensitive variable*

Abstract

The finite population proportion of a sensitive characteristic is estimated indirectly by using Randomized Response (RR) Techniques (RRT’s) pioneered by Warner (1965) followed by several other RRT’s in the literature. The existing literature contains several RRT’s for estimating the finite population mean of the sensitive quantitative variable. However, there might be a situation when the population proportion bearing the value of the stigmatizing variable below a threshold is of more concern than the exact population mean. The problem hence reduces to the estimation of the finite population distribution function of a quantitative sensitive variable. Following Chaudhuri and Saha (2004), a logistic regression approach has been used to estimate the finite population proportion bearing value of the stigmatizing variable below a threshold. As an alternative to this method, this article also attempts to provide suitable modifications for sensitive variables, in the estimation of distribution function proposed by Chaudhuri and Shaw (2020), when the variable of interest is innocuous. Numerical results based on a simulated population present interesting finding on the proposed methodologies.

Keywords:

• Empirical distribution function
• logistic regression
• randomized response
• stigmatizing quantitative variable
• unequal probability sampling

AMS Subject Classification:

• 62 DO5

Acknowledgments

The authors are thankful to the reviewer for providing useful comments which have helped in improving the manuscript.