Abstract
Group testing that tests groups with k experimental units instead of individuals has a long history and is very useful for estimating small proportion p under certain conditions. There are two sampling schemes for implementing group testing, one is Binomial sampling in which the number of groups n is predetermined, and another one is negative binomial sampling where the total number n of groups with a trait is predetermined. Many estimators including both the frequentist and Bayesian estimator have been proposed. The performance of all these estimators certainly depends on n and k. For the Bayesian estimators it also depends on the hyper-parameter \(\beta \) in the prior distribution \(Beta(1, \beta )\) of the proportion p. The present article studies the limits of all these estimators when n, or k, or \(\beta \) goes to infinity. The obtained results may be helpful with selecting n, k, and \(\beta \).
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Mi, J. Some limit results in estimation of proportion based on group testing. Metrika 82, 1021–1038 (2019). https://doi.org/10.1007/s00184-019-00719-4
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DOI: https://doi.org/10.1007/s00184-019-00719-4