Robust estimation in the multivariate normal model

Agnieszka Kulawik; Stefan Zontek

Discussiones Mathematicae Probability and Statistics (2016)

  • Volume: 36, Issue: 1-2, page 53-66
  • ISSN: 1509-9423

Abstract

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Robust estimation presented in the following paper is based on Fisher consistent and Fréchet differentiable statistical functionals. The method has been used in the multivariate normal model with variance components [5]. To transfer the method to estimate vector of expectations and positive definite covariance matrix of the multivariate normal model it is required to express the covariance matrix as a linear combination of basic elements of the vector space of real, square and symmetric matrices. The theoretical results have been completed with computer simulation studies. The robust estimator has been investigated both for model and contaminated data. Comparison with the maximum likelihood estimator has also been included.

How to cite

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Agnieszka Kulawik, and Stefan Zontek. "Robust estimation in the multivariate normal model." Discussiones Mathematicae Probability and Statistics 36.1-2 (2016): 53-66. <http://eudml.org/doc/286904>.

@article{AgnieszkaKulawik2016,
abstract = {Robust estimation presented in the following paper is based on Fisher consistent and Fréchet differentiable statistical functionals. The method has been used in the multivariate normal model with variance components [5]. To transfer the method to estimate vector of expectations and positive definite covariance matrix of the multivariate normal model it is required to express the covariance matrix as a linear combination of basic elements of the vector space of real, square and symmetric matrices. The theoretical results have been completed with computer simulation studies. The robust estimator has been investigated both for model and contaminated data. Comparison with the maximum likelihood estimator has also been included.},
author = {Agnieszka Kulawik, Stefan Zontek},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {asymptotic normality; Fisher consistency; Fréchet differentiability; multivariate normal model; statistical functional; multivariate robust estimation},
language = {eng},
number = {1-2},
pages = {53-66},
title = {Robust estimation in the multivariate normal model},
url = {http://eudml.org/doc/286904},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Agnieszka Kulawik
AU - Stefan Zontek
TI - Robust estimation in the multivariate normal model
JO - Discussiones Mathematicae Probability and Statistics
PY - 2016
VL - 36
IS - 1-2
SP - 53
EP - 66
AB - Robust estimation presented in the following paper is based on Fisher consistent and Fréchet differentiable statistical functionals. The method has been used in the multivariate normal model with variance components [5]. To transfer the method to estimate vector of expectations and positive definite covariance matrix of the multivariate normal model it is required to express the covariance matrix as a linear combination of basic elements of the vector space of real, square and symmetric matrices. The theoretical results have been completed with computer simulation studies. The robust estimator has been investigated both for model and contaminated data. Comparison with the maximum likelihood estimator has also been included.
LA - eng
KW - asymptotic normality; Fisher consistency; Fréchet differentiability; multivariate normal model; statistical functional; multivariate robust estimation
UR - http://eudml.org/doc/286904
ER -

References

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  1. [1] B.R. Clarke, Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations, Ann. Statist. 11 (4) (1983), 1196-1205. Zbl0541.62023
  2. [2] T. Bednarski and S. Zontek, Robust estimation of parameters in a mixed unbalanced model, Ann. Statist. 24 (4) (1996), 1493-1510. Zbl0878.62024
  3. [3] P.J. Huber, Robust Statistics (Wiley, New York, 1981). Zbl0536.62025
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  5. [5] A. Kulawik and S. Zontek, Robust estimation in the multivariate normal model with variance components, Statistics 49 (4), 766-780. Zbl1328.62315
  6. [6] R.A. Maronna, Robust M-estimators of multivariate location and scatter, Ann. Statist. 4 (1) (1976), 51-67. Zbl0322.62054
  7. [7] P.J. Rousseeuw, Multivariate estimation with high breakdown point, Mathematical Statistics and Applications, Vol. B (Bad Tatzmannsdorf, 1983), (Reidel, Dordrecht, 1985), 283-297. 
  8. [8] R. Zmyślony and S. Zontek, Robust M-estimator of parameters in variance components model, Discuss. Math. Probability and Statistics 22 (2002), 61-71. Zbl1037.62022
  9. [9] S. Zontek, Multivariate robust estimation in linear model for spatially located sensors and random input, Discuss. Math. Algebra and Stochastic Methods 18 (1998), 195-206. Zbl0946.62059

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