Mean Estimation of Sensitive Variables Under Non-response and Measurement Errors Using Optional RRT Models
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Mean Estimation of Sensitive Variables Under Non‑response and Measurement Errors Using Optional RRT Models Qi Zhang1 · Sadia Khalil2 · Sat Gupta1 Accepted: 2 October 2020 © Grace Scientific Publishing 2020
Abstract This study focuses on three issues we face in survey sampling: non-response, measurement errors, and social desirability bias. We propose a generalized mean estimator in the presence of measurement errors and non-response using optional RRT methodology under simple random sampling. We present a comparison of the proposed estimator with some commonly used estimators. Keywords Non-response · Measurement errors · Optional RRT models · Mean square error
1 Introduction Nowadays, many researchers use email or phone surveys which is an easier, cheaper, and faster way to obtain information. However, it causes a high non-response rate. This reduces the accuracy of parameter estimates. Among all the sampling methods, face-to-face interview is one that reduces non-response rate the most, but the cost is considerably higher than other methods. Hansen and Hurwitz [11] were the first to suggest a procedure of taking a subsample of non-respondents after the first email or phone attempt and then obtaining information from this group by personal interview. * Qi Zhang [email protected] Sadia Khalil [email protected] Sat Gupta [email protected] 1
Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA
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Department of Statistics, Lahore College for Women University, Lahore 54000, Pakistan
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Vol.:(0123456789)
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Page 2 of 15
Journal of Statistical Theory and Practice
(2021) 15:3
The problem of non-response has been discussed in many papers. Many researchers suggested different types of estimators for population parameters based on Hansen and Hurwitz [11] double sampling plan. Another method to increase the accuracy of population estimates is by using auxiliary information. Studies of mean estimation using information on auxiliary variables include Khare and Srivastava [14], Rao [22], Khare and Sinha [15–17], Kumar and Singh [19], Yaqub et al. [28], Bhushan and Pandey [3, 4], and Unal and Kadilar [26]. Hansen and Hurwitz [11] method could obtain more information from face-toface interview in the second phase, but it may also cause non-response bias if the variable of interest is sensitive in nature. The respondents are unlikely to provide true response in face-to-face interview for such questions. To reduce the social desirability bias (SDB) caused by sensitive questions, one could use randomized response technique (RRT) models when we target the group of non-respondents. Subjects may refuse to respond on the first call but may provide scrambled response on the second call with personal interview. Diana et al. [6] proposed an unbiased population mean estimator under this two-phase sampling. Their estimator reduces non-response but increases the estimator variance due to the use of RRT model in the non-respondent group. Later, Ahm
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