Comparison of Cramer-Rao lower bounds of variances for at least equal protection of respondents

In this paper, a new randomized response model is proposed, which is shown to have a Cramer–Rao lower bound of variance that is lower than the Cramer–Rao lower bound of variance suggested by Singh and Sedory at equal protection or greater protection of respondents. A new measure of protection of res...

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Bibliographic Details
Published in:Statistica Neerlandica 2016-05, Vol.70 (2), p.80-99
Main Authors: Lee, Cheon-Sig, Su, Shu-Ching, Mondragon, Katrina, Salinas, Veronica I., Zamora, Monique L., Sedory, Stephen Andrew, Singh, Sarjinder
Format: Article
Language:English
Subjects:
Alcohols
Devices
Drunk driving
Estimates
estimation of proportion
Lower bounds
Mathematical analysis
maximum likelihood estimation
randomized response sampling
relative efficiency and protection of respondents
Samples
Sampling
Statistical methods
Statistics
Students
Studies
Variance
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Summary:In this paper, a new randomized response model is proposed, which is shown to have a Cramer–Rao lower bound of variance that is lower than the Cramer–Rao lower bound of variance suggested by Singh and Sedory at equal protection or greater protection of respondents. A new measure of protection of respondents in the setup of the efficient use of two decks of cards, because of Odumade and Singh, is also suggested. The developed Cramer–Rao lower bounds of variances are compared under different situations through exact numerical illustrations. Survey data to estimate the proportion of students who have sometimes driven a vehicle after drinking alcohol and feeling over the legal limit are collected by using the proposed randomization device and then analyzed. The proposed randomized response technique is also compared with a black box technique within the same survey. A method to determine minimum sample size in randomized response sampling based on a small pilot survey is also given.
ISSN:0039-0402
1467-9574
DOI:10.1111/stan.12073