Bias Correction in Generalized Linear Models
Bias Correction in Generalized Linear Models
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DOI：
10.1111/j.2517-6161.1991.tb01852.x
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发表时间：
1991-07
期刊：
影响因子：
--
通讯作者：
G. Cordeiro;P. McCullagh
中科院分区：
文献类型：
--
作者：
G. Cordeiro;P. McCullagh
摘要 在本文中，我们推导了广义线性模型中线性参数、线性预测变量、离散参数和拟合值的最大似然估计的一阶偏差的一般公式。这些公式可以在 GLIM 程序中实现，以通过补充加权回归以最小的努力计算 n - 1 阶的偏差校正最大似然估计，其中 n 是样本大小。对于线性 Logistic 模型，结果表明 j8 的渐近偏差向量几乎与 f3 共线。推导出逻辑模型中 S 偏差的近似公式 flp/m+，其中 p = dim($) 且 m+ = E mi 是二项式指数之和，并进行数值验证。
SUMMARY In this paper we derive general formulae for first-order biases of maximum likelihood estimates of the linear parameters, linear predictors, the dispersion parameter and fitted values in generalized linear models. These formulae may be implemented in the GLIM program to compute bias-corrected maximum likelihood estimates to order n - 1, where n is the sample size, with minimal effort by means of a supplementary weighted regression. For linear logistic models it is shown that the asymptotic bias vector of j8 is almost collinear with f3. The approximate formula flp/m+ for the bias of S in logistic models, where p = dim($) and m+ = E mi is the sum of the binomial indices, is derived and checked numerically.