The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Natural Exponential Families with Quadratic Variance Functions
Open accessAbstract
The normal, Poisson, gamma, binomial, and negative binomial distributions are univariate natural exponential families with quadratic variance functions (the variance is at most a quadratic function of the mean). Only one other such family exists. Much theory is unified for these six natural exponential families by appeal to their quadratic variance property, including infinite divisibility, cumulants, orthogonal polynomials, large deviations, and limits in distribution.
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Citations
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
Parametric empirical Bayes inference: theory and applications
Morris, C. N. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477920 · Cited by 1,448
Stein's Estimation Rule and its Competitors—An Empirical Bayes Approach
Efron, B., & Morris, C. (1973) · Journal of the American Statistical Association · doi:10.1080/01621459.1973.10481350 · Cited by 981
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Cited by
Parametric empirical Bayes inference: theory and applications
Morris, C. N. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477920 · Cited by 1,448
Combinatorial Stochastic Processes
(2006) · Lecture Notes in Mathematics · doi:10.1007/b11601500 · Cited by 935
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
An extended quasi-likelihood function
NELDER, J. A., & PREGIBON, D. (1987) · Biometrika · doi:10.1093/biomet/74.2.221 · Cited by 414
Metadata
- Authors
- Morris, C. N.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1982-03-01
- Volume
- 10
- Issue
- 1
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2046338987
- Cited by
- 617
- References
- 3
- FWCI
- 3.79
- Type
- journal article
- Language
- en
- Open access
- bronze
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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.
