Use of correlated scrambling variables in quantitative randomized response technique

In this paper, we develop a new methodology that indicates that the use of correlated scrambling variables in the randomized response technique may play an important role in increasing the efficiency of an estimator of the population mean of a sensitive variable. Although it is clear analytically that the proposed estimator is more efficient than its existing competitors, we have investigated the magnitude of the gain in efficiency through simulation studies that involve both real secondary data from the health sciences, as well as artificial data. We also derive an estimator of the variance of the proposed estimator of mean and we study the coverage of 95% confidence intervals based on this variance estimator. An application using real primary data on smoking by university students is also included.