期刊
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
卷 46, 期 7, 页码 3290-3296出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2013.851241
关键词
Nuisance tangent space; Regression model; Semiparametric model
资金
- NIH [R01 HL094786]
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 non parametrically estimated along with themean. In contrast, estimation and inferences using misspecified error distributions or variance functions are generally not efficient.
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