1974/01/01 by R. W. M. Wedderburn · 11 citations
Mathematics · Agricultural and Biological Sciences · #Advanced Statistical Methods and Models #Genetics and Plant Breeding #Statistical Methods and Bayesian Inference
paper · doi:10.1093/biomet/61.3.439
openalex publication_date 1974/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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).