On Efficacies of Dalenius-Vitale Technique with Compulsory Versus Optional Randomized Responses from Complex Surveys

Dalenius and Vitale (1974) gave a Randomized Response (RR) Technique (RRT) to unbiasedly estimate the mean of a real variable relating to sensitive issues concerned with a finite population of individuals from whom a simple random sample (SRS) is taken with replacement (WR). Chaudhuri (2002) modified it to cover the general cases of unequal probability sampling schemes. Here we extend it to a still more general case when option is allowed for direct responses (DR) from those people in a part of a complex sample to whom the issues do not appear sensitive enough. With simulations from data certain specific cases are illustrated for a comparison of efficiencies.