Orthogonality of the mean and error distribution in generalized linear models

Huang, Alan and Rathouz, Paul J. (2017) Orthogonality of the mean and error distribution in generalized linear models. Communications in Statistics - Theory and Methods, 46 7: 3290-3296. doi:10.1080/03610926.2013.851241


Author Huang, Alan
Rathouz, Paul J.
Title Orthogonality of the mean and error distribution in generalized linear models
Journal name Communications in Statistics - Theory and Methods   Check publisher's open access policy
ISSN 0361-0926
1532-415X
Publication date 2017-01-01
Year available 2016
Sub-type Article (original research)
DOI 10.1080/03610926.2013.851241
Open Access Status Not yet assessed
Volume 46
Issue 7
Start page 3290
End page 3296
Total pages 7
Place of publication Philadelphia, United States
Publisher Taylor & Francis
Language eng
Formatted 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.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
HERDC Pre-Audit
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 0 times in Thomson Reuters Web of Science Article
Scopus Citation Count Cited 0 times in Scopus Article
Google Scholar Search Google Scholar
Created: Fri, 21 Mar 2014, 02:37:55 EST by Kay Mackie on behalf of School of Mathematics & Physics