On the Chao and Zelterman estimators in a binomial mixture model |
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| Institution: | 1. College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha, Hunan, China;2. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada;1. Department of Statistics, Seoul National University, Seoul, Republic of Korea;2. Korea University Business School, Seoul, Republic of Korea;1. Department of Anesthesiology, General Intensive Care and Pain Medicine, Medical University of Vienna, Vienna, Austria;2. Christian Doppler Laboratory for Cardiac and Thoracic Diagnosis and Regeneration, Medical University of Vienna, Vienna, Austria;3. RAIC Laboratory 13C1, Medical University of Vienna, Vienna, Austria;4. Division of Nephrology and Dialysis, Department of Medicine III, Medical University of Vienna, Vienna, Austria;5. Department of Cardiothoracic Surgery, Medical University of Vienna, Vienna, Austria;1. Médecins Sans Frontières, Khayelitsha, Cape Town, South Africa;2. School of Public Health, University of Cape Town, Cape Town, South Africa;3. Médecins Sans Frontières, South African Mission, Cape Town, South Africa;4. Department of Global Health and Social Medicine, Harvard Medical School, Boston, MA 02115, USA |
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| Abstract: | Data from a surveillance system can be used to estimate the size of a disease population. For certain surveillance systems, a binomial mixture model arises as a natural choice. The Chao estimator estimates a lower bound of the population size. The Zelterman estimator estimates a parameter that is neither a lower bound nor an upper bound. By comparing the Chao estimator and the Zelterman estimator both theoretically and numerically, we conclude that the Chao estimator is better. |
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| Keywords: | Capture–recapture Population size |
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