Robust m-estimator of parameters in variance components model

Roman Zmyślony; Stefan Zontek

Discussiones Mathematicae Probability and Statistics (2002)

  • Volume: 22, Issue: 1-2, page 61-71
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Roman Zmyślony, and Stefan Zontek. "Robust m-estimator of parameters in variance components model." Discussiones Mathematicae Probability and Statistics 22.1-2 (2002): 61-71. <http://eudml.org/doc/287637>.

@article{RomanZmyślony2002,
abstract = {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.},
author = {Roman Zmyślony, Stefan Zontek},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Robust estimator; maximum likelihood estimator; statistical functional; Fisher consistency; Fréchet differentiability; robust estimator},
language = {eng},
number = {1-2},
pages = {61-71},
title = {Robust m-estimator of parameters in variance components model},
url = {http://eudml.org/doc/287637},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Roman Zmyślony
AU - Stefan Zontek
TI - Robust m-estimator of parameters in variance components model
JO - Discussiones Mathematicae Probability and Statistics
PY - 2002
VL - 22
IS - 1-2
SP - 61
EP - 71
AB - 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.
LA - eng
KW - Robust estimator; maximum likelihood estimator; statistical functional; Fisher consistency; Fréchet differentiability; robust estimator
UR - http://eudml.org/doc/287637
ER -

References

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  1. [1] T. Bednarski, Fréchet differentiability and robust estimation, Asymptotic Statistics. Proc. of the Fifth Prague Symp. Physica Verlag, Springer, (1994), 49-58. 
  2. [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. Zbl0733.62026
  3. [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. Zbl0798.62043
  4. [4] T. Bednarski and Z. Zontek, Robust estimation of parameters in mixed unbalanced models, Ann. Statist. 24 (4) (1996), 1493-1510. Zbl0878.62024
  5. [5] B.R. Clarke, Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations, Ann. Statist. 11 (1983), 1196-1206. Zbl0541.62023
  6. [6] B.R. Clarke, Nonsmooth analysis and Fréchet differentiability of M-functionals, Probab. Th. Rel. Fields 73 (1986), 197-209. Zbl0581.60005
  7. [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. [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. Zbl0119.34904
  9. [9] D.M. Rocke, Robustness and balance in the mixed model, Biometrics 47 (1991), 303-309. 
  10. [10] J. Seely, Quadratic subspaces and completness, Ann. Math. Statist. 42 (1971), 710-721. Zbl0249.62067
  11. [11] R. Zmyślony and H. Drygas, Jordan algebras and Bayesian quadratic estimation of variance components, Linear Algebra and its Applications 168 (1992), 259-275. Zbl0760.62068

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