Bias reduction in exponential family nonlinear models
Bias reduction in exponential family nonlinear models
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DOI：
10.1093/biomet/asp055
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发表时间：
2009-12-01
期刊：
影响因子：
2.7
通讯作者：
Firth, David
中科院分区：
文献类型：
--
作者：
Kosmidis, Ioannis;Firth, David
在Firth（1993，Biometrika）中，展示了如何通过调整得分向量来移除最大似然估计的渐近偏差中的前导项，并且在典型链接广义线性模型中，该方法等效于最大化惩罚似然，这很容易通过数据的迭代调整来实现。在这里，一个更一般的家庭的偏差减少调整是一个广泛的一类单变量和多变量广义非线性模型。调整后的得分向量的公式计算方便，在单变量模型中，它们直接建议通过数据调整的迭代方案来实现。对于广义线性模型，给出了该方法存在惩罚似然解释的充分必要条件。古德曼行列关联模型的一个说明性应用程序显示了如何计算的简单性和统计效益的偏差减少扩展到广义线性模型。
In Firth (1993, Biometrika) it was shown how the leading term in the asymptotic bias of the maximum likelihood estimator is removed by adjusting the score vector, and that in canonical-link generalized linear models the method is equivalent to maximizing a penalized likelihood that is easily implemented via iterative adjustment of the data. Here a more general family of bias-reducing adjustments is developed for a broad class of univariate and multivariate generalized nonlinear models. The resulting formulae for the adjusted score vector are computationally convenient, and in univariate models they directly suggest implementation through an iterative scheme of data adjustment. For generalized linear models a necessary and sufficient condition is given for the existence of a penalized likelihood interpretation of the method. An illustrative application to the Goodman row-column association model shows how the computational simplicity and statistical benefits of bias reduction extend beyond generalized linear models.