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

Mariusz Grządziel

ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

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

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.

Keywords

ENG

variance component, linear mixed model, maximum likelihood

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.
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.
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.
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.
G. Golub and C. Van Loan, Matrix Computations, 4th Edition (The John Hopkins University Press, Baltimore, 2013).
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.
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.
J. Jiang, Linear and Generalized Linear Mixed Models and Their Applications (Springer, New York, 2007). doi: 10.1007/978-0-387-47946-0.
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.
C. R. Rao and J. Kleffe, Estimation of Variance Components and Applications (North Holland, New York, 1988). doi: 10.1002/bimj.4710320518.
C. R. Rao and H. Toutenburg, Linear Models: Least Squares and Alternatives, 2nd Edition (Springer, New York, 1999).

Title

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

Affiliations

Abstract

Keywords

Bibliography