Article ID Journal Published Year Pages File Type
1154163 Statistics & Probability Letters 2007 7 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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