Hepworth Graham, Biggerstaff Brad J
School of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia,
Centers for Disease Control and Prevention, Fort Collins, CO 80521, USA.
J Agric Biol Environ Stat. 2017 Dec;22(4):602-614. doi: 10.1007/s13253-017-0297-2. Epub 2017 Aug 1.
In the estimation of proportions by pooled testing, the MLE is biased, and several methods of correcting the bias have been presented in previous studies. We propose a new estimator based on the bias correction method introduced by Firth (Biometrika 80:27-38, 1993), which uses a modification of the score function, and we provide an easily computable, Newton-Raphson iterative formula for its computation. Our proposed estimator is almost unbiased across a range of problems, and superior to existing methods. We show that for equal pool sizes the new estimator is equivalent to the estimator proposed by Burrows (Phytopathology 77:363-365, 1987). The performance of our estimator is examined using pooled testing problems encountered in plant disease assessment and prevalence estimation of mosquito-borne viruses.
在通过混合检测估计比例时，极大似然估计（MLE）存在偏差，先前的研究中已经提出了几种校正偏差的方法。我们基于Firth（《生物统计学》80:27 - 38，1993）引入的偏差校正方法提出了一种新的估计器，该方法使用了得分函数的修正，并且我们为其计算提供了一个易于计算的牛顿 - 拉弗森迭代公式。我们提出的估计器在一系列问题中几乎是无偏的，并且优于现有方法。我们表明，对于相等的池大小，新估计器等同于Burrows（《植物病理学》77:363 - 365，1987）提出的估计器。我们使用植物病害评估和蚊媒病毒流行率估计中遇到的混合检测问题来检验我们估计器的性能。
