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Robust estimation in the multivariate normal model

100%
Kulawik A., Zontek S.
Discussiones Mathematicae Probability and Statistics
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2016
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tom 36
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nr 1-2
53-66
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.
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Robust m-estimator of parameters in variance components model

100%
Zmyślony R., Zontek S.
Discussiones Mathematicae Probability and Statistics
|
2002
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tom 22
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nr 1-2
61-71
EN
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.
3
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On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters

100%
Neumann K., Zontek S.
Discussiones Mathematicae Probability and Statistics
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2006
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tom 26
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nr 2
109-125
EN
We consider the problem of admissible quadratic estimation of a linear function of μ² and σ² in n dimensional normal model N(Kμ,σ²Iₙ) under quadratic risk function. After reducing this problem to admissible estimation of a linear function of two quadratic forms, the set of admissible estimators are characterized by giving formulae on the boundary of the set D ⊂ R² of components of the two quadratic forms constituting the set of admissible estimators. Different shapes and topological properties of the set D are studied.
4
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On optimality of the orthogonal block design

100%
Synówka-Bejenka E., Zontek S.
Discussiones Mathematicae Probability and Statistics
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2012
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tom 32
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nr 1-2
59-68
EN
In the paper a usual block design with treatment effects fixed and block effects random is considered. To compare experimental design the asymptotic covariance matrix of a robust estimator proposed by Bednarski and Zontek (1996) for simultaneous estimation of shift and scale parameters is used. Asymptotically A- and D- optimal block designs in the class of designs with bounded block sizes are characterized.
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