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Exponential Dispersion Models
Abstract
SUMMARY: We study general properties of the class of exponential dispersion models, which is the multivariate generalization of the error distribution of Nelder and Wedderburn’s (1972) generalized linear models. Since any given moment generating function generates an exponential dispersion model, there exists a multitude of exponential dispersion models, and some new examples are introduced. General results on convolution and asymptotic normality of exponential dispersion models are presented. Asymptotic theory is discussed, including a new small-dispersion asymptotic framework, which extends the domain of application of large-sample theory. Procedures for constructing new exponential dispersion models for correlated data are introduced, including models for longitudinal data and variance components. The results of the paper unify and generalize standard results for distributions such as the Poisson, the binomial, the negative binomial, the normal, the gamma, and the inverse Gaussian distributions.
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Cites
Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method
WEDDERBURN, R. W. M. (1974) · Biometrika · doi:10.1093/biomet/61.3.439 · Cited by 2,122
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Breslow, N. E., & Clayton, D. G. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10594284 · Cited by 4,629
Double Exponential Families and Their Use in Generalized Linear Regression
Efron, B. (1986) · Journal of the American Statistical Association · doi:10.1080/01621459.1986.10478327 · Cited by 451
A Coefficient of Determination for Generalized Linear Models
Zhang, D. (2017) · The American Statistician · doi:10.1080/00031305.2016.1256839 · Cited by 444
Testing for Overdispersion in Poisson and Binomial Regression Models
Dean, C. B. (1992) · Journal of the American Statistical Association · doi:10.1080/01621459.1992.10475225 · Cited by 386
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Waldron, A., Miller, D. C., Redding, D., Mooers, A., Kuhn, T. S., Nibbelink, N., Roberts, J. T., Tobias, J. A., & Gittleman, J. L. (2017) · Nature · doi:10.1038/nature24295 · Cited by 369
Metadata
- Authors
- Jørgensen, B.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1987-01-01
- Volume
- 49
- Issue
- 2
- Pages
- 127-145
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2465940576
- Cited by
- 679
- References
- 1
- FWCI
- 8.99
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
