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2014 | 34 | 1-2 | 187-197
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
34
Numer
1-2
Strony
187-197
Opis fizyczny
Daty
wydano
2014
otrzymano
2014-10-18
poprawiono
2014-11-26
Twórcy
  • Department of Mathematics, Wrocław University of Environmental and Life Sciences, Grunwaldzka 53, 50-357 Wrocław, Poland
Bibliografia
  • [1] R. Christensen, Plane answers to complex questions: the theory of linear models, 4th Edition (Springer, New York, 2011). doi: 10.1007/978-1-4419-9816-3.
  • [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.
  • [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.
  • [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.
  • [5] G. Golub and C. Van Loan, Matrix Computations, 4th Edition (The John Hopkins University Press, Baltimore, 2013).
  • [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.
  • [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] J. Jiang, Linear and Generalized Linear Mixed Models and Their Applications (Springer, New York, 2007). doi: 10.1007/978-0-387-47946-0.
  • [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.
  • [10] C. R. Rao and J. Kleffe, Estimation of Variance Components and Applications (North Holland, New York, 1988). doi: 10.1002/bimj.4710320518.
  • [11] C. R. Rao and H. Toutenburg, Linear Models: Least Squares and Alternatives, 2nd Edition (Springer, New York, 1999).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1165
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