Forcibly re-scrambled randomized response model for simultaneous estimation of means of two sensitive variables (Q1988275)

For estimating the population mean of a sensitive character, a multiplicative randomized response technique (RRT) has been introduced in the literature which consists of a scrambled response \( Z_i = s Y_i \), where \(Y_i\) is the sensitive value of the \(i \)-th unit of the population and \(s\) is a scrambling variable having a known distribution. Following this, several extensions have been proposed which include the estimation of population means of two sensitive characters using a scrambled response and another pseudo-response. The authors of the present work consider the problem of simultaneous estimation of population means of two sensitive quantitative characters. This is done by the use of a forced quantitative RRT under a further scrambling of the already scrambled responses. Performance of the suggested model is studied analytically and empirically towards the end of the paper by simulation. The analytical study involves heavy algebra in view of the model chosen and comparisons depend on the choice of unknown parameters. The empirical simulation study, however, does not show much of a gain over the previous study. Prompted by this, the practical user may tend to choose an alternative of using known methods for each of the two sensitive quantitative variables separately. The paper has a good review in the introduction and has a good collection of references enabling further studies.