%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 }