Bayesian bounds for population proportion under ranked set sampling. (English) Zbl 07551446
Summary: In this article, we consider a dichotomous population characterized by the parameter \(p\) defined as the proportion of individuals in the population possessing certain characteristic. The unknown proportion \(p\) is our parameter of interest in the present work. Under the assumption that \(p\) is a random quantity we derive a Bayesian Crammer-Rao (BCR) bound in connection with the estimation of \(p\). The proposed procedure is based on a ranked set sample (RSS) observed on the variable of interest which is binary in nature. This RSS-based approach is compared with its corresponding SRS (simple random sample) counterpart in the cases of both perfect and imperfect rankings. The proposed procedure is applied for estimating the proportion of children aged \(12--23\) months (to the mothers aged 15–49 years of rural India) who are not immunized with the vaccine against measles using National Family Health Survey-3 (2005–2006) data of India.
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