On efficacy of empirical Bayes estimation of a finite population mean of a sensitive variable through randomized responses

In a social survey an unequal probability sample is supposedly at hand. The problem of utilizing it to estimate the finite population mean of a stigmatizing variable has a known solution admitting assessment of accuracy level. Here we examine improvement by Empirical Bayes procedure, exploiting available data on a correlated variable while using a randomized response technique to gather data on the main variable of interest.