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A note on quasi-likelihood for exponential families

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  • Annis, David H.

Abstract

Maximum likelihood estimation for exponential families depends exclusively on the first two moments of the data. Recognizing this, Wedderburn [1974. Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61, 439-447] proposed estimating regression parameters based on a quasi-likelihood function requiring only the relationship between the mean and variance. We extend quasi-likelihood to situations in which there exists vague prior information on the mean parameters. It is shown when data are exponential family with quadratic variance functions, maximum a posteriori inference under a conjugate prior relies solely on two moments of the data and the prior distribution. This result suggests a Bayesian analog of quasi-likelihood for which only two moments of the data and two moments of the prior need be specified.

Suggested Citation

  • Annis, David H., 2007. "A note on quasi-likelihood for exponential families," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 431-437, February.
  • Handle: RePEc:eee:stapro:v:77:y:2007:i:4:p:431-437
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    Cited by:

    1. Nguyen, Truc T. & Chen, John T., 2009. "A connection between the double gamma model and Laplace sample mean," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1305-1310, May.

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