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On a formula for the distribution of the maximum likelihood estimator
Abstract
A simple formula for the conditional distribution of the maximum likelihood estimator given a maximal ancillary statistic is discussed and exemplified. The formula is generally accurate to order $ O(n^{-1}) $ or even $ O(n^{-{3}/{2}}) $, and for many important models it is, in fact, exact. After some preliminary discussion of the formula and of certain relevant aspects of likelihood, the formula is used to motivate the definition of a modified profile likelihood whose inferential properties are illustrated. The question of when the distribution formula is exact is considered, and in this connexion several new examples of exactness, including a bivariate generalization of the inverse Gaussian distribution, are adduced. The formula is shown also to be exact for arbitrary transformation models. To prove this it has been necessary to extend the basic theory of transformation models to cover the cases where the group action is not free. This extension, which appears of interest in itself, also allows of a generalization of a useful formula for the marginal likelihood for the index parameter of a composite transformation model.
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Cites
Nelder, J. A., & Wedderburn, R. W. M. (1972) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2344614 · Cited by 7,194
Consistent Estimates Based on Partially Consistent Observations
Neyman, J., & Scott, E. L. (1948) · Econometrica · doi:10.2307/1914288 · Cited by 2,691
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
Theory of Group Representations and Applications
Barut, A., & Raczka, R. (1986) · WORLD SCIENTIFIC eBooks · doi:10.1142/0352 · Cited by 1,426
Saddlepoint Approximations in Statistics
Daniels, H. E. (1954) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728652 · Cited by 1,106
Two new properties of mathematical likelihood
Fisher, R. A. (1934) · Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1934.0050 · Cited by 481
Information and Exponential Families: In Statistical Theory
Barndorff-Nielsen, O. E. (2014) · Wiley series in probability and statistics · doi:10.1002/9781118857281 · Cited by 434
Self-citationStatistical Properties of Inverse Gaussian Distributions. II
Tweedie, M. C. K. (1957) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177706881 · Cited by 383
Fraser, D. A. S. (1968) · Medical Entomology and Zoology · Cited by 360
Theory of Probability (3rd Edition)
Litton, C. D. (1984) · Journal of the Operational Research Society · doi:10.1057/jors.1984.141 · Cited by 282
Cited by
Rue, H., Martino, S., & Chopin, N. (2009) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00700.x · Cited by 5,279
Bias reduction of maximum likelihood estimates
FIRTH, D. (1993) · Biometrika · doi:10.1093/biomet/80.1.27 · Cited by 5,035
Bootstrap confidence intervals
DiCiccio, T. J., & Efron, B. (1996) · Statistical Science · doi:10.1214/ss/1032280214 · Cited by 2,286
Weighted Likelihood Estimation of Ability in Item Response Theory
Warm, T. A. (1989) · Psychometrika · doi:10.1007/bf02294627 · Cited by 1,216
Dawid, A. P. (1984) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2981683 · Cited by 1,085
Metadata
- Authors
- BARNDORFF-NIELSEN, O.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1983-08-01
- Volume
- 70
- Issue
- 2
- Pages
- 343-365
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2161364915
- Cited by
- 466
- References
- 17
- FWCI
- 7.79
- 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).
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