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Estimating the components of a mixture of normal distributions
Abstract
The problem of estimating the components of a mixture of two normal distributions, multivariate or otherwise, with common but unknown covariance matrices is examined. The maximum likelihood equations are shown to be not unduly laborious to solve and the sampling properties of the resulting estimates are investigated, mainly by simulation. Moment estimators, minimum χ2 and Bayes estimators are discussed but they appear greatly inferior to maximum likelihood except in the univariate case, the inferiority lying either in the sampling properties of the estimates or in the complexity of the computation. The wider problems obtained by allowing the components in the mixture to have different covariance matrices, or by having more than two components in the mixture, are briefly discussed, as is the relevance of this problem to cluster analysis.
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Citations
Cited by
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
“methods for finite mixtures of parametric families, variance components and hyperparameters in Bayesian prior distributions of parameters. In addition, the EM algorithm corresponds to certain robust estimation techniques based on iteratively reweighted least squares. We anticipate that recognition of the EM algorithm…”
BackgroundMethodInfluentialMcLachlan, G., & Peel, D. (2000) · Wiley Series in Probability and Statistics · doi:10.1002/0471721182 · Cited by 10,991
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
An Approach for Determining the Number of Clusters in a Model-Based Cluster Analysis
Akogul, S., & Erisoglu, M. (2017) · Entropy · doi:10.3390/e19090452 · Cited by 269
Bimodality, dimensionality, and the notion of hypnotic types
Balthazard, C. G., & Woody, E. Z. (1989) · International Journal of Clinical and Experimental Hypnosis · doi:10.1080/00207148908410534 · Cited by 34
Metadata
- Authors
- DAY, N. E.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1969
- Volume
- 56
- Issue
- 3
- Pages
- 463-474
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W1966502880
- Cited by
- 824
- References
- 0
- FWCI
- 10.77
- Type
- journal article
- Language
- en
- Open access
- closed
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