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Quasi-Likelihood Functions, Generalized Linear Models, and the Gauss-Newton Method

R. W. M. Wedderburn
Biometrika
Vol. 61, No. 3 (Dec., 1974), pp. 439-447
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2334725
Stable URL: http://www.jstor.org/stable/2334725
Page Count: 9
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Quasi-Likelihood Functions, Generalized Linear Models, and the Gauss-Newton Method
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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).

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