Taking clue from pioneer work of Chen and Singh (J Mod Appl Stat Methods 11:105–122, 2012), we have suggested a generalized RR procedure, for estimating the multinomial proportions of potentially sensitive attributes in survey sampling, using higher order moments of scrambling variables at the estimation stage to produce unbiased estimators. The RR procedure due to Chen and Singh (J Mod Appl Stat Methods 11:105–122, 2012) is viewed as member of the proposed RR procedure. Expressions for variance and covariance of the suggested generalized estimator with its development are derived. It is found that the developed estimator is more efficient than Warner’s (J Am Stat Assoc 60:63–69, 1965) RRT. A numerical illustration is also given in support of the present study.
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