Abstract
This paper suggests a stratified Kuk model to estimate the proportion of sensitive attributes of a population composed by a number of strata; this is undertaken by applying stratified sampling to the adjusted Kuk model. The paper estimates sensitive parameters when the size of the stratum is known by taking proportional and optimal allocation methods into account and then extends to the case of an unknown stratum size, estimating sensitive parameters by applying stratified double sampling and checking the two allocation methods. Finally, the paper compares the efficiency of the proposed model to that of the Su, Sedory and Singh model and the adjusted Kuk model in terms of the estimator variance.
Highlights
Warner (1965) was the first person to suggest an ingenious survey model called the randomized response model (RRM) to obtain sensitive information from respondents without disturbing their privacy by using a randomization device that contained the following two questions: Q1:Do you have a sensitive attribute A?, Q2:Do you have a nonsensitive attribute Ac? (with probability (1 − P ).The probability of a “yes” answer is given by θW ∗ = P π + (1 − P )(1 − π). (1)Let nθW ∗ be the number of “yes” responses in a sample of size n respondents, and the estimator πW and the variance V of its sensitive proportion π are respectively πW = θW ∗ − (1 P), P 1/2, (2)
This paper considers the conditions to estimate the proportion of sensitive attributes of a population composed by a number of strata and extends the adjusted Kuk model by applying stratified sampling
This paper estimate sensitive attributes of a population composed of a number of strata by applying stratified sampling to the Su, Sedory and Singh model
Summary
Warner (1965) was the first person to suggest an ingenious survey model called the randomized response model (RRM) to obtain sensitive information from respondents without disturbing their privacy by using a randomization device that contained the following two questions (a sensitive question and a nonsensitive one): Q1:Do you have a sensitive attribute A? (with probability P ), Q2:Do you have a nonsensitive attribute Ac? (with probability (1 − P ). Let nθK∗ denote the number of “yes” responses in the sample of size n, and the estimator πK of π, the proportion of the population in the sensitive group, and its variance V (πK ) are given by πK θK∗ θ1. Su et al (2015) model estimates sensitive attributes by using simple random sampling, and it is difficult to apply it to populations composed of several strata. This paper considers the conditions to estimate the proportion of sensitive attributes of a population composed by a number of strata and extends the adjusted Kuk model by applying stratified sampling. The paper estimates sensitive parameters in the case of a known stratum size by taking proportional and optimal allocation methods into account It extends it to the case of an unknown stratum size by estimating sensitive parameters by applying stratified double sampling to the Su, Sedory, and Singh model and checking the two allocation methods. The paper compares the efficiency of the proposed model to that of the Su, Sedory and Singh model and the stratified Kuk model in terms of the estimator variance
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