Randomized response: Estimating mean square errors of linear estimators and finding optimal unbiased strategies |
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Authors: | Dr A Chaudhuri |
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Institution: | (1) Indian Statistical Institute, 203, Barrackpore Trunk Road, 700035 Calcutta, India |
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Abstract: | Summary General procedures are described to generate quantitative randomized response (RR) required to estimate the finite population
total of a sensitive variable. Permitting sample selection with arbitrary probabilities a formula for the mean square error
(MSE) of a linear estimator of total based on RR is noted indicating the simple modification over one that might be based
on direct response (DR) if the latter were available. A general formula for an unbiased estimator of the MSE is presented.
A simple approximation is proposed in case the RR ratio estimator is employed based on a simple random sample (SRS) taken
without replacement (WOR). Among sampling strategies employing unbiased but not necessarily linear estimators based on RR,
certain optimal ones are identified under two alternative models analogously to well-known counterparts based on DR, if available.
Unlike Warner’s (1965) treatment of categorical RR we consider quantitative RR here. |
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Keywords: | Finite population Linear estimator Mean square error estimation Randomized response Unbiased optimal strategies Varying probability sampling |
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