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Tytuł artykułu

Robust estimation in the multivariate normal model

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EN
Abstrakty
EN
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.
Twórcy
  • Institute of Mathematics, University of Silesia, 40-007 Katowice, Bankowa 14, Poland
  • Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, 65-516 Zielona Góra, Szafrana 4A, Poland
Bibliografia
  • [1] B.R. Clarke, Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations, Ann. Statist. 11 (4) (1983), 1196-1205.
  • [2] T. Bednarski and S. Zontek, Robust estimation of parameters in a mixed unbalanced model, Ann. Statist. 24 (4) (1996), 1493-1510.
  • [3] P.J. Huber, Robust Statistics (Wiley, New York, 1981).
  • [4] 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.
  • [5] A. Kulawik and S. Zontek, Robust estimation in the multivariate normal model with variance components, Statistics 49 (4), 766-780.
  • [6] R.A. Maronna, Robust M-estimators of multivariate location and scatter, Ann. Statist. 4 (1) (1976), 51-67.
  • [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] R. Zmyślony and S. Zontek, Robust M-estimator of parameters in variance components model, Discuss. Math. Probability and Statistics 22 (2002), 61-71.
  • [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.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1184
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