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Výpočet těsných mezí pro divergenceí
Harremoes, P. ; Vajda, Igor
The paper presents a general method for evaluation of the joint range of pairs of f-divergences. This range provides tight maxima and minima for one f-divergence for given value of the other. Applications in information theory, identification and detection are mentioned.
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Několik aplikací divergenčního kriteria ve spojitých rodinách
Broniatowski, M. ; Vajda, Igor
Power subdivergence, power superdivergence, power pseudodistance and Renyi pseudodistance are introduced as statistical point estimation criteria.Basic theory of the corresponding four types of estimators including the Fisher consistency and influence curves is presented. Explicit formulas are obtained for estimators of location and scale used in the research of diploma and PhD students.
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Zobecnění Devrouye-Lugosiho teorému
Berlinet, A. ; Vajda, Igor
Estimation of distributions of stochastic models is studied and adaptive selection of a better of two estimates is considered. Devroye and Lugosi's recent book on this topic established a theorem on the total variation error of a selection rule proposed by them. We extended this theorem to arbitrary metric divergence errors, and also to more general alternative selection rules.
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Asymptotické vlastnosti intervalových statistik
Vajda, Igor ; van der Meulen, E. C.
This is a continuation of our previous paper dealing with simple spacings. Here we deal with arbitrary m-spacings. We introduce new spacings statistics measuring divergence of hypothetical and empirical distributions. It is proved that they are asymptotically equivalent with all spacings statistics known from the literature. General asymptotic equivalence of this type is a new result with interesting applications.
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