The problem of estimation of a proportion of a sensitive character using a randomization device in survey sampling
نویسندگان
چکیده
The problem of estimation of a proportion of a sensitive character using a randomization device in survey sampling is well known since Warner (1965). A detailed review and applications of such techniques can be found in Fox and Tracy (1986). Following Gjestvang and Singh (2006), let and be two known positive real numbers. Gjestvang and Singh (2009) considered a new additive model in which each respondent in the sample is requested to draw a card secretly from a well-shuffled deck of cards. In the deck, let p be the proportion of cards bearing the statement, “Multiply scrambling variable S with and add to the real value of the sensitive variable i Y ” , and (1 ) p be the proportion of cards bearing the statement, “Multiply scrambling variable S with and subtract it from the real value of the sensitive variable i Y .” Mathematically, each respondent is requested to report the scrambled response i Z as:
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