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Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance
Open accessAbstract
We show that in the mixed model of the analysis of variance, there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal, and efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix. These results follow directly by an application of a general result of Weiss (1971, 1973) concerning maximum likelihood estimates. This problem differs from standard problems in that we do not have independent, identically distributed observations and that estimates of different parameters may require normalizing sequences of different orders of magnitude. We give some examples and comment briefly on likelihood ratio tests for these models.
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Cited by
Self, S. G., & Liang, K.-Y. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478472 · Cited by 2,661
A Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models
Chung, Y., Rabe-Hesketh, S., Dorie, V., Gelman, A., & Liu, J. (2013) · Psychometrika · doi:10.1007/s11336-013-9328-2 · Cited by 554
Pinheiro, J. C., Liu, C., & Wu, Y. N. (2001) · Journal of Computational and Graphical Statistics · doi:10.1198/10618600152628059 · Cited by 287
A note on the asymptotic distribution of likelihood ratio tests to test variance components
Visscher, P. M. (2006) · Twin Research and Human Genetics · doi:10.1375/twin.9.4.490 · Cited by 169
Cedersund, G., & Roll, J. (2009) · The FEBS Journal · doi:10.1111/j.1742-4658.2008.06845.x · Cited by 127
Metadata
- Authors
- Miller, J. J.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1977-07-01
- Volume
- 5
- Issue
- 4
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1999947197
- Cited by
- 193
- References
- 0
- FWCI
- 3.32
- Type
- journal article
- Language
- en
- Open access
- bronze
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