On maximum likelihood estimation in mixed normal models with two variance components

Mariusz Grządziel

Discussiones Mathematicae Probability and Statistics (2014)

  • Volume: 34, Issue: 1-2, page 187-197
  • ISSN: 1509-9423

Abstract

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In the paper we deal with the problem of parameter estimation in the linear normal mixed model with two variance components. We present solutions to the problem of finding the global maximizer of the likelihood function and to the problem of finding the global maximizer of the REML likelihood function in this model.

How to cite

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Mariusz Grządziel. "On maximum likelihood estimation in mixed normal models with two variance components." Discussiones Mathematicae Probability and Statistics 34.1-2 (2014): 187-197. <http://eudml.org/doc/271046>.

@article{MariuszGrządziel2014,
abstract = {In the paper we deal with the problem of parameter estimation in the linear normal mixed model with two variance components. We present solutions to the problem of finding the global maximizer of the likelihood function and to the problem of finding the global maximizer of the REML likelihood function in this model.},
author = {Mariusz Grządziel},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {variance component; linear mixed model; maximum likelihood},
language = {eng},
number = {1-2},
pages = {187-197},
title = {On maximum likelihood estimation in mixed normal models with two variance components},
url = {http://eudml.org/doc/271046},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Mariusz Grządziel
TI - On maximum likelihood estimation in mixed normal models with two variance components
JO - Discussiones Mathematicae Probability and Statistics
PY - 2014
VL - 34
IS - 1-2
SP - 187
EP - 197
AB - In the paper we deal with the problem of parameter estimation in the linear normal mixed model with two variance components. We present solutions to the problem of finding the global maximizer of the likelihood function and to the problem of finding the global maximizer of the REML likelihood function in this model.
LA - eng
KW - variance component; linear mixed model; maximum likelihood
UR - http://eudml.org/doc/271046
ER -

References

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  2. [2] 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
  3. [3] S. Gnot, A. Michalski and A. Urbańska-Motyka, On some properties of ML and REML estimators in mixed normal models with two variance components, Discuss. Math. Prob. and Stat. 24 (2004) 109-126. Zbl1052.62029
  4. [4] S. Gnot, D. Stemann, G. Trenkler and A. Urbańska-Motyka, Maximum likelihood estimation in mixed normal models with two variance components, Statistics 36 (2002) 283-302. doi: 10.1080/02331880213197. Zbl1003.62017
  5. [5] G. Golub and C. Van Loan, Matrix Computations, 4th Edition (The John Hopkins University Press, Baltimore, 2013). Zbl1268.65037
  6. [6] E. Gross, M. Drton and S. Petrović, Maximum likelihood degree of variance components models, Electronic J. Stat. 6 (2012) 993-1016. doi: 10.1214/12-EJS702. Zbl1281.62159
  7. [7] M. Grządziel and A. Michalski, A note on the existence of maximum likelihood estimates in variance components models, accepted for publication in Discuss. Math. Prob. and Stat. 2014. 
  8. [8] J. Jiang, Linear and Generalized Linear Mixed Models and Their Applications (Springer, New York, 2007). doi: 10.1007/978-0-387-47946-0. Zbl1152.62040
  9. [9] A. Olsen, J. Seely and D. Birkes, Invariant quadratic estimation for two variance components, Ann. Stat. 4 (1976) 878-890. doi: 10.1214/aos/1176343586. Zbl0344.62060
  10. [10] C. R. Rao and J. Kleffe, Estimation of Variance Components and Applications (North Holland, New York, 1988). doi: 10.1002/bimj.4710320518. Zbl0645.62073
  11. [11] C. R. Rao and H. Toutenburg, Linear Models: Least Squares and Alternatives, 2nd Edition (Springer, New York, 1999). Zbl0846.62049

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