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2019 Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model
Gregory Haber, Yaakov Malinovsky
Electron. J. Statist. 13(2): 2624-2657 (2019). DOI: 10.1214/19-EJS1583


Estimation of a single Bernoulli parameter using pooled sampling is among the oldest problems in the group testing literature. To carry out such estimation, an array of efficient estimators have been introduced covering a wide range of situations routinely encountered in applications. More recently, there has been growing interest in using group testing to simultaneously estimate the joint probabilities of two correlated traits using a multinomial model. Unfortunately, basic estimation results, such as the maximum likelihood estimator (MLE), have not been adequately addressed in the literature for such cases. In this paper, we show that finding the MLE for this problem is equivalent to maximizing a multinomial likelihood with a restricted parameter space. A solution using the EM algorithm is presented which is guaranteed to converge to the global maximizer, even on the boundary of the parameter space. Two additional closed form estimators are presented with the goal of minimizing the bias and/or mean square error. The methods are illustrated by considering an application to the joint estimation of transmission prevalence for two strains of the Potato virus Y by the aphid Myzus persicae.


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Gregory Haber. Yaakov Malinovsky. "Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model." Electron. J. Statist. 13 (2) 2624 - 2657, 2019.


Received: 1 July 2018; Published: 2019
First available in Project Euclid: 14 August 2019

zbMATH: 07104726
MathSciNet: MR3992500
Digital Object Identifier: 10.1214/19-EJS1583


Vol.13 • No. 2 • 2019
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