A Probability Proportional to Size Estimation of a Rare Sensitive Attribute Using a Partial Randomized Response Model with Poisson Distribution

Gi-Sung Lee, Ki-Hak Hong and Chang-Kyoon Son ()
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Gi-Sung Lee: Department of Children Welfare, Woosuk University, Wanju 55338, Republic of Korea
Ki-Hak Hong: Department of Computer Science, Dongshin University, Naju 58245, Republic of Korea
Chang-Kyoon Son: Department of Applied Statistics, Dongguk University, Gyeongju 38066, Republic of Korea

Mathematics, 2024, vol. 12, issue 2, 1-11

Abstract: In this paper, we suggest using a partial randomized response model using Poisson distribution to efficiently estimate a rare sensitive attribute by applying the probability proportional to size (PPS) sampling method when the population is composed of several different and sensitive clusters. We have obtained estimators for a rare and sensitive attribute and their variances and variance estimates by applying PPS sampling and two-stage equal probability sampling. We compare the efficiency between the estimators of the rare sensitive attribute, one obtained via PPS sampling with replacement and the other obtained using the two-stage equal probability sampling with replacement. As a result, it is confirmed that the estimate obtained via the PPS sampling with replacement is more efficient than the estimate provided by the two-stage equal probability sampling with replacement when the cluster sizes are different.

Keywords: Poisson distribution; partial randomized response model; rare sensitive attribute; cluster sampling; probability proportional to size (PPS) sampling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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