Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model
| Autor: | Yaakov Malinovsky, Gregory Haber |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences Mean squared error Bernoulli parameter Parameter space 01 natural sciences Article Methodology (stat.ME) 010104 statistics & probability Joint probability distribution 0502 economics and business Expectation–maximization algorithm Statistics pooled sampling restricted parameter space 0101 mathematics EM algorithm Statistics - Methodology 050205 econometrics Mathematics group testing estimation 05 social sciences Estimator Sampling (statistics) maximum likelihood estimator multinomial sampling Group testing Multinomial distribution Statistics Probability and Uncertainty |
| Zdroj: | Electron J Stat Electron. J. Statist. 13, no. 2 (2019), 2624-2657 |
| Popis: | 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. Comment: Submitted for publication |
| Databáze: | OpenAIRE |
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