A note on the existence of the maximum likelihood estimate in variance components models

Mariusz Grządziel; Andrzej Michalski

ArticleOriginal scientific text

Title

A note on the existence of the maximum likelihood estimate in variance components models

Authors ¹, ¹

Affiliations

Department of Mathematics, Wrocław University of Environmental and Life Sciences, Grunwaldzka 53, 50-357 Wrocław, Poland

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.

Keywords

ENG

variance component, linear mixed model, maximum likelihood

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.
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.
J. Jiang, Linear and Generalized Linear Mixed Models and Their Applications (Springer, Dordrecht, 2007). doi: 10.1007/978-0-387-47946-0.
C.R. Rao, Linear statistical inference and its applications (Wiley, New York, 1973). doi: 10.1002/9780470316436.

Title

A note on the existence of the maximum likelihood estimate in variance components models

Affiliations

Abstract

Keywords

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