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Consistent Estimation of a Mixing Distribution
Open accessAbstract
A maximum-penalized-likelihood method is proposed for estimating a mixing distribution and it is shown that this method produces a consistent estimator, in the sense of weak convergence. In particular, a new proof of the consistency of maximum-likelihood estimators is given. The estimated number of components is shown to be at least as large as the true number, for large samples. Also, the large-sample limits of estimators which are constrained to have a fixed finite number of components are identified as distributions minimizing Kullback-Leibler divergence from the true mixing distribution. Estimation of a Poisson mixture distribution is illustrated using the distribution of traffic accidents presented by Simar.
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Cites
Nonparametric maximum likelihood estimation of a mixing distribution
Laird, N. (1978) · Journal of the American Statistical Association · doi:10.1080/01621459.1978.10480103 · Cited by 753
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Sensitivity and specificity of information criteria
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Modeling Uncertainty in Latent Class Membership: A Case Study in Criminology
Roeder, K., Lynch, K. G., & Nagin, D. S. (1999) · Journal of the American Statistical Association · doi:10.1080/01621459.1999.10474179 · Cited by 342
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Watkins, L. P., & Yang, H. (2005) · The Journal of Physical Chemistry B · doi:10.1021/jp0467548 · Cited by 340
Metadata
- Authors
- Leroux, B. G.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1992-09-01
- Volume
- 20
- Issue
- 3
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1963566461
- Cited by
- 413
- References
- 1
- FWCI
- 2.24
- Type
- journal article
- Language
- en
- Open access
- bronze
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