Orthogonality of the mean and error distribution in generalized linear models. Issue 7 (3rd April 2017)

• Record Type: Journal Article
• Authors: Huang, Alan; Rathouz, Paul J.
• Is Part Of: Communications in statistics. Volume 46:Issue 7(2017)
• Page Start: 3290
• Page End: 3296
• Publication Date: 2017-04-03
• Subjects: Nuisance tangent space -- Regression model -- Semiparametric model; 62J12; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.851241
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: 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 the mean. In contrast, estimation and inferences using misspecified error distributions or variance functions are generally not efficient.