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A note on the existence of the maximum likelihood estimate in variance components models
Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 159-167.

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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.
Keywords: variance component, linear mixed model, maximum likelihood 
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Grządziel, Mariusz; Michalski, Andrzej. A note on the existence of the maximum likelihood estimate in variance components models. Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 159-167. http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a10/

[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.

[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.

[3] J. Jiang, Linear and Generalized Linear Mixed Models and Their Applications (Springer, Dordrecht, 2007). doi: 10.1007/978-0-387-47946-0.

[4] C.R. Rao, Linear statistical inference and its applications (Wiley, New York, 1973). doi: 10.1002/9780470316436.