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An extended quasi-likelihood function. (English) Zbl 0621.62078
The introduction by R. W. M. Wedderburn [Biometrika 61, 439-447 (1974; Zbl 0292.62050)] of quasi-likelihood for general linear models greatly widened their scope by allowing the full distributional assumption about the random component in the models to be replaced by a much weaker assumption in which only the first and second moments were defined.
The present authors introduce an extended quasi-likelihood function which allows for the comparison of various forms of all the components of a generalized linear model, i.e. the linear predictor, the link function, and the variance function. The theory is illustrated by three examples.
Reviewer: A.N.Philippou

MSC:
62J99 Linear inference, regression
62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)
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