To define a likelihood we have to specify the form of distribution of the observations, but to define a quasi-likelihood function we need only specify a relation between the mean and variance of the observations and the quasi-likelihood can then be used for estimation. For a one-parameter exponential family the log likelihood is the same as the quasi-likelihood and it follows that assuming a one-parameter exponential family is the weakest sort of distributional assumption that can be made. The Gauss-Newton method for calculating nonlinear least squares estimates generalizes easily to deal with maximum quasi-likelihood estimates, and a rearrangement of this produces a generalization of the method described by Nelder & Wedderburn (1972).
%0 Journal Article
%1 wedderburn_quasi-likelihood_1974
%A Wedderburn, R. W. M
%D 1974
%J Biometrika
%K Exponential Gauss-Newton Generalized Quasi-likelihood families, likelihood, linear maximum method, models,
%N 3
%P 439--447
%R 10.1093/biomet/61.3.439
%T Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method
%U http://biomet.oxfordjournals.org/content/61/3/439
%V 61
%X To define a likelihood we have to specify the form of distribution of the observations, but to define a quasi-likelihood function we need only specify a relation between the mean and variance of the observations and the quasi-likelihood can then be used for estimation. For a one-parameter exponential family the log likelihood is the same as the quasi-likelihood and it follows that assuming a one-parameter exponential family is the weakest sort of distributional assumption that can be made. The Gauss-Newton method for calculating nonlinear least squares estimates generalizes easily to deal with maximum quasi-likelihood estimates, and a rearrangement of this produces a generalization of the method described by Nelder & Wedderburn (1972).
@article{wedderburn_quasi-likelihood_1974,
abstract = {To define a likelihood we have to specify the form of distribution of the observations, but to define a quasi-likelihood function we need only specify a relation between the mean and variance of the observations and the quasi-likelihood can then be used for estimation. For a one-parameter exponential family the log likelihood is the same as the quasi-likelihood and it follows that assuming a one-parameter exponential family is the weakest sort of distributional assumption that can be made. The Gauss-Newton method for calculating nonlinear least squares estimates generalizes easily to deal with maximum quasi-likelihood estimates, and a rearrangement of this produces a generalization of the method described by Nelder \& Wedderburn (1972).},
added-at = {2017-01-09T13:57:26.000+0100},
author = {Wedderburn, R. W. M},
biburl = {https://www.bibsonomy.org/bibtex/23080e4a3f00db457db30b08de102f4ba/yourwelcome},
doi = {10.1093/biomet/61.3.439},
interhash = {6ebc239c51f1d56e55df59cf5d756861},
intrahash = {3080e4a3f00db457db30b08de102f4ba},
issn = {0006-3444, 1464-3510},
journal = {Biometrika},
keywords = {Exponential Gauss-Newton Generalized Quasi-likelihood families, likelihood, linear maximum method, models,},
language = {en},
month = dec,
number = 3,
pages = {439--447},
timestamp = {2017-01-09T14:01:11.000+0100},
title = {Quasi-likelihood functions, generalized linear models, and the {Gauss}—{Newton} method},
url = {http://biomet.oxfordjournals.org/content/61/3/439},
urldate = {2012-03-01},
volume = 61,
year = 1974
}