广义线性模型中均值和误差分布的渐近性
Orthogonality of the mean and error distribution in generalized linear models
摘要：
证明了在广义线性模型中，平均模型参数总是与误差分布正交。因此，无论误差分布是完全已知的，还是已知参数的有限向量，或者完全未指定，平均模型参数的极大似然估计量都将是渐近有效的，在这种情况下，似然被认为是适当的半参数似然。此外，平均模型参数的极大似然估计将渐近独立于误差分布的极大似然估计。这概括了一些著名的结果的特殊情况下，正常的，伽玛和多项式回归模型，也许更有趣的是，表明，渐近有效的估计和推断总是可以得到的，如果误差分布是nonparametrically估计的平均值。相比之下，使用错误指定的误差分布或方差函数的估计和推断通常不是有效的。
英文摘要：
We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the error distribution is known completely, known up to a finite vector of parameters, or left completely unspecified, in which case the likelihood is taken to be an appropriate semiparametric likelihood. Moreover, the maximum likelihood estimator of the mean-model parameter will be asymptotically independent of the maximum likelihood estimator of the error distribution. This generalizes some well-known results for the special cases of normal, gamma and multinomial regression models, and, perhaps more interestingly, suggests that asymptotically efficient estimation and inferences can always be obtained if the error distribution is nonparametrically estimated along with the mean. In contrast, estimation and inferences using misspecified error distributions or variance functions are generally not efficient.
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