Why We Need One More Monograph on Randomized Response
Chapter 2. Warner (1965) in his pioneering model to tackle the problem of gathering trustworthy data relating to dichotomous sensitive information on a human feature A and its complement Ac, essentially recommended approaching a person to be sampled in a community, with a box containing a certain number of indistinguishable cards of which a proportion p(0 < p ≠ 1/2 < 1) is marked A and the rest marked Ac. The person on request is required to draw a “random” card and respond by answering “Yes” for a “match” between the card type and the person’s own real characteristic or a “No” for a “nonmatch” before returning the card to the box. No matter how a sample is chosen it is possible to derive, for every person labeled i, which is 1, …, N with a value yi as 1 if i bears the characteristic A, or o if the characteristic is Ac, an unbiased estimator ri instead of yi, with a variance in terms of p, with respect to the randomization experiment involved in data gathering. Warner restricted exclusively to samples chosen by SRSWR taking an RR by the above method independently every time a person is chosen randomly. Here we briefly consider a current development with variations in estimation procedures, taking account of the units that are distinct using only one RR, from the person or all the RRs separately generated every time the person appears in the sample, keeping the total number of draws in the sample intact or the number of draws are allowed to continue till a predetermined number of distinct units appear in the sample. This theoretical exercise is motivated because in the context of DR surveys, Basu (1958), Pathak (1962), Des Raj and Khamis (1958), Lanke (1975a), Chikkagoudar (1966), Asok (1980) among others, developed detailed theories of estimation with these three aspects of SRSWR.