Robust m-estimator of parameters in variance components model
Discussiones Mathematicae. Probability and Statistics, Tome 22 (2002) no. 1-2, pp. 61-71.

Voir la notice de l'article provenant de la source Library of Science

It is shown that a method of robust estimation in a two way crossed classification mixed model, recently proposed by Bednarski and Zontek (1996), can be extended to a more general case of variance components model with commutative a covariance matrices.
Keywords: Robust estimator, maximum likelihood estimator, statistical functional, Fisher consistency, Fréchet differentiability
@article{DMPS_2002_22_1-2_a5,
     author = {Zmy\'slony, Roman and Zontek, Stefan},
     title = {Robust m-estimator of parameters in variance components model},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {61--71},
     publisher = {mathdoc},
     volume = {22},
     number = {1-2},
     year = {2002},
     zbl = {1037.62022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2002_22_1-2_a5/}
}
TY  - JOUR
AU  - Zmyślony, Roman
AU  - Zontek, Stefan
TI  - Robust m-estimator of parameters in variance components model
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2002
SP  - 61
EP  - 71
VL  - 22
IS  - 1-2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2002_22_1-2_a5/
LA  - en
ID  - DMPS_2002_22_1-2_a5
ER  - 
%0 Journal Article
%A Zmyślony, Roman
%A Zontek, Stefan
%T Robust m-estimator of parameters in variance components model
%J Discussiones Mathematicae. Probability and Statistics
%D 2002
%P 61-71
%V 22
%N 1-2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2002_22_1-2_a5/
%G en
%F DMPS_2002_22_1-2_a5
Zmyślony, Roman; Zontek, Stefan. Robust m-estimator of parameters in variance components model. Discussiones Mathematicae. Probability and Statistics, Tome 22 (2002) no. 1-2, pp. 61-71. http://geodesic.mathdoc.fr/item/DMPS_2002_22_1-2_a5/

[1] T. Bednarski, Fréchet differentiability and robust estimation, Asymptotic Statistics. Proc. of the Fifth Prague Symp. Physica Verlag, Springer, (1994), 49-58.

[2] T. Bednarski, B.R. Clarke and W. Kokiewicz, Statistical expansions and locally uniform Fréchet differentiability, J. Australian Math. Soc., Ser. A 50 (1991), 88-97.

[3] T. Bednarski and B.R. Clarke, Trimmed likelihood estimation of location and scale of the normal distribution, Australian J. Statists. 35 (1993), 141-153.

[4] T. Bednarski and Z. Zontek, Robust estimation of parameters in mixed unbalanced models, Ann. Statist. 24 (4) (1996), 1493-1510.

[5] B.R. Clarke, Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations, Ann. Statist. 11 (1983), 1196-1206.

[6] B.R. Clarke, Nonsmooth analysis and Fréchet differentiability of M-functionals, Probab. Th. Rel. Fields 73 (1986), 197-209.

[7] B. Iglewicz, Robust scale estimators and confidence intervals for location, D.C. Hoagling, F. Mosteller and J.W. Tukey, Eds., Understanding Robust and Exploratory Data Analysis, Wiley, New York, (1983), 404-431.

[8] J. Kiefer, On large deviations of the empiric D.F. of vector chance variables and a law of iterated logarithm, Pacific J. Math. 11 (1961), 649-660.

[9] D.M. Rocke, Robustness and balance in the mixed model, Biometrics 47 (1991), 303-309.

[10] J. Seely, Quadratic subspaces and completness, Ann. Math. Statist. 42 (1971), 710-721.

[11] R. Zmyślony and H. Drygas, Jordan algebras and Bayesian quadratic estimation of variance components, Linear Algebra and its Applications 168 (1992), 259-275.