Cramer–Rao Lower Bounds of Variance for Estimating Two Proportions and Their Overlap by Using Two Decks of Cards

Lee, C.-S.; Sedory, Stephen A.; Singh, Sarjinder

doi:10.1016/bs.host.2016.01.020

Cited by 6 publications

(5 citation statements)

References 3 publications

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“…Again following Lee et al (2016), Xu et al (2021), and Olanipekun et al (2023), the likelihood function L * is given by…”

Section: Cramer-rao Lower Bounds Of Variances For the Model-iimentioning

confidence: 99%

See 1 more Smart Citation

New Randomised Response Models for Two Sensitive Characteristics: Theory and Application

Naatjes,

Sedory,

Singh

2023

Int Statistical Rev

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SummaryIn this paper, we introduce two new randomised response models for estimating the prevalence of two sensitive characteristics and their overlap in a population by making use of a single deck of cards. The proposed models ensure the privacy of the respondents and also reduce the burden on the respondents as they require the random selection of only one card from a deck of cards each of which contains a pair of questions that are to be answered in order. The variance expressions of the proposed estimators are derived and matched to their Cramer–Rao lower bounds of variances. A simulation study has been carried out to compare the proposed models to each other for least protection. Lastly, a real survey application, related to the acceptability of the vaccines produced by Pfizer and Moderna is included. We had findings in Summer 2021 similar to those of the Harvard Study done in December 2021, which was based on a half‐million data values, that shows the cost effectiveness of the survey design.

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“…Again following Lee et al (2016), Xu et al (2021), and Olanipekun et al (2023), the likelihood function L * is given by…”

Section: Cramer-rao Lower Bounds Of Variances For the Model-iimentioning

confidence: 99%

“…Again following Lee et al (2016), Xu et al (2021), and Olanipekun et al (2023), the likelihood function

L^{*}

is given by

L^{*} = ((), \begin{matrix} center \\ array n \\ array n_{11}^{*}, n_{10}^{*}, n_{01}^{*}, n_{00}^{*} \end{matrix}) {false(λ_{11}^{*} false)}^{n_{11}^{*}} {false(λ_{10}^{*} false)}^{n_{10}^{*}} {false(λ_{01}^{*} false)}^{n_{01}^{*}} {false(λ_{00}^{*} false)}^{n_{00}^{*}}

…”

Section: Cramer–rao Lower Bounds Of Variances For the Model‐iimentioning

confidence: 99%

New Randomised Response Models for Two Sensitive Characteristics: Theory and Application

Naatjes,

Sedory,

Singh

2023

Int Statistical Rev

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“…In this section, following Lee et al. (2016a), we will discuss the maximum likelihood estimates of

π_{A}

π_{A}

, and

π_{B}

and develop the Cramer–Rao lower bounds for variance and covariance of proposed model.…”

Section: Cramer–rao Lower Bound Of Variancementioning

confidence: 99%

Two sensitive characteristics and their overlap with two questions per card

Sedory

Singh

2021

Biometrical J

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“…The proposed Bayesian RRT method is not only able to deal with the RRT case, but also applicable to estimating covariance matrices with incomplete data information semiparametrically. It would also be interesting to investigate the Cramer-Rao lower bound (Singh and Sedory, 2011;Lee et al, 2016) for continuous responses in further research.…”

Section: Rrt Questionmentioning

confidence: 99%

Bayesian randomized response technique with multiple sensitive attributes: The case of information systems resource misuse

Chung¹,

Chu²,

So³

2018

Ann. Appl. Stat.

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The randomized response technique (RRT) is a classical and effective method used to mitigate the distortion arising from dishonest answers. The traditional RRT usually focuses on the case of a single sensitive attribute, and discussion of the case of multiple sensitive attributes is limited. Here, we study a business case to identify some individual and organizational determinants driving information systems (IS) resource misuse in the workplace. People who actually engage in IS resource misuse are probably not willing to provide honest answers, given the sensitivity of the topic. Yet, to develop the causal relationship between IS resource misuse and its determinants, a version of the RRT for multivariate analysis is required. To implement the RRT with multiple sensitive attributes, we propose a Bayesian approach for estimating covariance matrices with incomplete information (resulting from the randomization procedure in the RRT case). The proposed approach (i) accommodates the positive definite condition and other intrinsic parameter constraints in the posterior to improve statistical precision, (ii) incorporates Bayesian shrinkage estimation for covariance matrices despite incomplete information, and (iii) adopts a quasi-likelihood method to achieve Bayesian semiparametric inference for enhancing flexibility. We show the effectiveness of the proposed method in a simulation study. We also apply the Bayesian RRT method and structural equation modeling to identify the causal relationship between IS resource misuse and its determinants.

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Cramer–Rao Lower Bounds of Variance for Estimating Two Proportions and Their Overlap by Using Two Decks of Cards

Cited by 6 publications

References 3 publications

New Randomised Response Models for Two Sensitive Characteristics: Theory and Application

New Randomised Response Models for Two Sensitive Characteristics: Theory and Application

Two sensitive characteristics and their overlap with two questions per card

Bayesian randomized response technique with multiple sensitive attributes: The case of information systems resource misuse

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