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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 1

Improved estimation of mean in randomized response models

Zawar HUSSAİN
Javid SHABBIR
Pages
91–104
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The proposed estimator has been compared with the Ryu et al. and Hussain and Shabbir (Improved estimation procedure for the mean of a sensitive variable using randomized response model, Pakistan Journal of Statistics 25(2), 205–220, 2009) estimators assuming simple random sampling with replacement.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The present investigation considers the problem of estimating the mean of a sensitive quantitative variable μA in a human population survey, using the scrambled response technique suggested by Ryu, Kim, Heo and Park (On stratified randomized response sampling, Model Assisted Statistics and Application 1(1), 31–36, 2005–2006).
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Key Findings & Data:The optimum value of the de- gree k(0 $geq k geq$ 1) of the belief in the prior estimate depends, besides others, on the unknown population parameters, e.g. mean and vari- ance, so the proposed family of estimators may have limited practical applications.
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Conclusion & Impact:The proposed estimator has been compared with the Ryu et al. and Hussain and Shabbir (Improved estimation procedure for the mean of a sensitive variable using randomized response model, Pakistan Journal of Statistics 25(2), 205–220, 2009) estimators assuming simple random sampling with replacement.
🔬Design:Survey & Empirical Study
📍Scope:2005–2006 Verileri
⚙️Variables:Domain Parameters

Abstract

The present investigation considers the problem of estimating the mean of a sensitive quantitative variable μA in a human population survey, using the scrambled response technique suggested by Ryu, Kim, Heo and Park (On stratified randomized response sampling, Model Assisted Statistics and Application 1(1), 31–36, 2005–2006). Specifically, using the prior estimate (or guessed mean) of the mean of a population, a family of estimators μAk is presented to estimate the population mean μA, and its properties are examined. The optimum value of the de- gree k(0 $geq k geq$ 1) of the belief in the prior estimate depends, besides others, on the unknown population parameters, e.g. mean and vari- ance, so the proposed family of estimators may have limited practical applications. In an attempt to overcome this problem, another esti- mator based on the estimated optimum value of k has been proposed. The proposed estimator has been compared with the Ryu et al. and Hussain and Shabbir (Improved estimation procedure for the mean of a sensitive variable using randomized response model, Pakistan Journal of Statistics 25(2), 205–220, 2009) estimators assuming simple random sampling with replacement.

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Cite This Article

HUSSAİN, Z., SHABBIR, J. (2022). Improved estimation of mean in randomized response models. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 1, 91–104. https://ajindex.com/articles/530586

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