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Comparison of Cramer–Rao lower bounds of variances for at least equal protection of respondents
Author(s) -
Lee CheonSig,
Su ShuChing,
Mondragon Katrina,
Salinas Veronica I.,
Zamora Monique L.,
Sedory Stephen Andrew,
Singh Sarjinder
Publication year - 2016
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12073
Subject(s) - randomized response , cramér–rao bound , mathematics , statistics , variance (accounting) , upper and lower bounds , sample size determination , randomization , limit (mathematics) , econometrics , randomized controlled trial , maximum likelihood , medicine , mathematical analysis , accounting , surgery , estimator , business
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.