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Unbiased Estimation for Sensitive Items in Complex Surveys Permitting Direct or Scrambled Response

Sanghamitra Pal


Warner (1965) introduced the randomized response (RR) technique to estimate the unknown proportion of people bearing a sensitive characteristic like tax evasion, alcoholism etc. in a given community when a simple random sample (SRS) is chosen with replacement (WR). A spurt of research ensued as documented by numbers of published papers and a monograph by Chaudhuri and Mukerjee (1988). Mangat and Singh (1994) proposed an optional randomized response (ORR) technique allowing each respondent to opt either for direct response (DR) or randomized response (RR) to collect information on a stigmatizing quantitative character. As a direct response, the respondent may give out the true value relating to it. Otherwise, the interviewee may report the true value multiplied by a randomly chosen number having a known distribution. Then it is a randomized response, which is a scrambled response (Poole 1974; Eichhorn and Hayre 1983). The respondent is permitted not to divulge which of these two kinds of response is actually given out—direct or scrambled. The probability of choosing between a ¢direct’ and a ¢scrambled’ response should vary across individuals rather than be a constant. In this paper we propose an unbiased estimator of the total of a quantitative sensitive variable and also one for its variance for any general unequal probability sampling scheme permitting options for direct or scrambled responses.


scrambled responses, optional randomized response, varying probability sampling

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