Unbiased Variance Estimator of the Randomised Response Techniques for Population Mean

Abstract

Antoch, Mola and Vozár (2022) proposed recently new randomized response technique for population mean or total of a quantitative variable. The aim of the paper is to solve the open problem to derive unbiased variance estimator of these procedures. In their proposal, unlike other randomized response techniques for population mean or total the randomized response is not a linear function of a sensitive variable. However, standard techniques to derive variance estimators in this setting are based on this assumption. That is why an interviewer needs also to know values pseudorandom numbers (i.e., results of individual randomization experiments). Respondents might perceive this relaxation of privacy protection negative. The performance of the approximate two-sided confidence intervals of distributions with different shape including their coverage is assessed by a simulation study for simple random sampling without replacement.