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1
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A note on the functional law of the iterated logarithm for Lévy's area process

100%
Modeste N’zi, M’hamed Eddahbi
Applicationes Mathematicae
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1996-1997
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tom 24
|
nr 2
223-229
EN
By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.
2
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On maximum likelihood estimation in mixed normal models with two variance components

100%
Grządziel M.
Discussiones Mathematicae Probability and Statistics
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2014
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tom 34
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nr 1-2
187-197
EN
In the paper we deal with the problem of parameter estimation in the linear normal mixed model with two variance components. We present solutions to the problem of finding the global maximizer of the likelihood function and to the problem of finding the global maximizer of the REML likelihood function in this model.
3
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A note on the existence of the maximum likelihood estimate in variance components models

100%
Grządziel M., Michalski A.
Discussiones Mathematicae Probability and Statistics
|
2014
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tom 34
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nr 1-2
159-167
EN
In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhyā 61, 1999), giving a necessary and sufficient condition for the existence of the maximum likelihood estimate in this model, are pointed out and corrected. A new proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the existence of the REML estimate of variance components, is presented.
4
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Node assignment problem in Bayesian networks

100%
Polanska J., Borys D., Polanski A.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 2
233-240
EN
This paper deals with the problem of searching for the best assignments of random variables to nodes in a Bayesian network (BN) with a given topology. Likelihood functions for the studied BNs are formulated, methods for their maximization are described and, finally, the results of a study concerning the reliability of revealing BNs' roles are reported. The results of BN node assignments can be applied to problems of the analysis of gene expression profiles.
5
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Sensitivity analysis in linear models

88%
Liu S., Ma T., Liu Y.
Special Matrices
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2016
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tom 4
|
nr 1
225-232
EN
In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.
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