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