A note on the existence of the maximum likelihood estimate in variance components models
Mariusz Grządziel; Andrzej Michalski
Discussiones Mathematicae Probability and Statistics (2014)
- Volume: 34, Issue: 1-2, page 159-167
- ISSN: 1509-9423
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topMariusz Grządziel, and Andrzej Michalski. "A note on the existence of the maximum likelihood estimate in variance components models." Discussiones Mathematicae Probability and Statistics 34.1-2 (2014): 159-167. <http://eudml.org/doc/270963>.
@article{MariuszGrządziel2014,
abstract = {In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhyā 61, 1999), giving a necessary and sufficient condition for the existence of the maximum likelihood estimate in this model, are pointed out and corrected. A new proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the existence of the REML estimate of variance components, is presented.},
author = {Mariusz Grządziel, Andrzej Michalski},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {variance component; linear mixed model; maximum likelihood},
language = {eng},
number = {1-2},
pages = {159-167},
title = {A note on the existence of the maximum likelihood estimate in variance components models},
url = {http://eudml.org/doc/270963},
volume = {34},
year = {2014},
}
TY - JOUR
AU - Mariusz Grządziel
AU - Andrzej Michalski
TI - A note on the existence of the maximum likelihood estimate in variance components models
JO - Discussiones Mathematicae Probability and Statistics
PY - 2014
VL - 34
IS - 1-2
SP - 159
EP - 167
AB - In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhyā 61, 1999), giving a necessary and sufficient condition for the existence of the maximum likelihood estimate in this model, are pointed out and corrected. A new proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the existence of the REML estimate of variance components, is presented.
LA - eng
KW - variance component; linear mixed model; maximum likelihood
UR - http://eudml.org/doc/270963
ER -
References
top- [1] E. Demidenko and H. Massam, On the existence of the maximum likelihood estimate in variance components models, Sankhyā A. Methods and Techniques 61 (1999) 431-443. Zbl0972.62034
- [2] E. Gross, M. Drton and S. Petrović, Maximum likelihood degree of variance components models, Electronic Journal of Statistics 6 (2012) 993-1016. doi: 10.1214/12-EJS702. Zbl1281.62159
- [3] J. Jiang, Linear and Generalized Linear Mixed Models and Their Applications (Springer, Dordrecht, 2007). doi: 10.1007/978-0-387-47946-0. Zbl1152.62040
- [4] C.R. Rao, Linear statistical inference and its applications (Wiley, New York, 1973). doi: 10.1002/9780470316436.
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