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

• Autorzy: Mariusz Grządziel , Andrzej Michalski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

variance component; linear mixed model; maximum likelihood

Kategorie tematyczne

• 62J05: Linear regression
• 62F10: Point estimation

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2014
• Tom: 34
• Numer: 1-2
• Strony: 159-167

Daty

wydano

2014

otrzymano

2014-10-15

poprawiono

2014-11-25

Twórcy

autor

Mariusz Grządziel

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

autor

Andrzej Michalski

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmps1164