# 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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