Optimal rank set sampling estimates for a population proportion |
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| Institution: | 1. Department of Oral and Maxillofacial Surgery, Ninewells Hospital and Medical School, Dundee DD1 9SY, United Kingdom;2. Department of Orthodontics, Dundee Dental Hospital and School, Park Place, Dundee DD1 4HN, United Kingdom;1. Department of Oral Diagnosis, Piracicaba Dental School, University of Campinas, Piracicaba, Brazil;2. Department of Pathology, School of Dentistry, Federal University of Rio Grande do Sul, Porto Alegre, Brazil;3. Service of Buccal Pathology, João de Barros Barreto University Hospital, Federal University of Pará, Belém, Brazil;4. Oral Medicine Department, Sírio-Libanês Hospital, São Paulo, Brazil;5. Department of Pathology, A. C. Camargo Cancer Center, São Paulo, Brazil;6. Medical School, Clinics Hospital, University of São Paulo, São Paulo, Brazil;7. Department of Oral Surgery and Pathology, School of Dentistry, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil;1. Assistant Professor, Department of Pathology, Fortaleza University School of Medicine, Fortaleza, Brazil; PhD Student, Federal University of Ceara School of Dentistry, Fortaleza, Brazil;2. Associated Professor, Department of Dental Clinic, Discipline of Pediatric Dentistry, Federal University of Ceara School of Dentistry, Fortaleza, Brazil;3. PhD Student, Department of Dental Clinic, Federal University of Ceara School of Dentistry, Fortaleza, Brazil;4. Associated Professor, Department of Dental Clinic, Discipline of Oral and Maxillofacial Surgery and Stomatology, Federal University of Ceara School of Dentistry, Fortaleza, Brazil; Oral and Maxillofacial Surgeon, Department of Oral and Maxillofacial Surgery, Memorial Batista Hospital, Fortaleza, Brazil |
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| Abstract: | This paper examines two different classes of estimates for a population proportion based on an unbalanced rank set sample. Specifically, the two classes correspond to the maximum likelihood estimator (MLE) and a weighted average (WA) estimate. Both estimators are asymptotically normal, so standard inference procedures can still be implemented. Furthermore, these results can be used to develop optimal allocation schemes for both estimators. The performances of the optimal estimators are studied in terms of both finite sample and asymptotic relative efficiency. In general, the MLE is more efficient than the WA estimate. Lastly, the practicality of the optimal sampling plans is addressed and illustrated via an example. |
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