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Hugo Dionizy Steinhaus – droga do współczesnej teorii prawdopodobieństwa

100%
Bednarski T.
Acta Universitatis Lodziensis. Folia Oeconomica
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2018
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vol. 4
|
issue 336
61-70
EN
Hugo Steinhaus (1887–1972) studied mathematics and philosophy at the Jan Kazimierz University in Lwow. Since 1905 he stayed in Göttingen where in 1911 he obtained his PhD under David Hilbert. In 1920 he became professor of the Lwow University. Together with Stefan Banach he established there a strong mathematical center for functional analysis. After the II World War he participated in creation of the mathematics department of the Wroclaw University and he was a founder of Wroclaw school for applied probability. He is the author and coauthor of 250 publications. In 1923 H. Steinhaus published in “Fundamenta Mathematicae” a study of Borel countable probabilities where, among other things, he gave an axiomatic definition of a probability measure on the space of countable zero‑one sequences. The goal of this note is to demonstrate a potentially important role of Steinhaus result in the process leading to final axiomatization of probability theory by Andrei Kolmogorov in 1933.
PL
Hugo Steinhaus (1887–1972) ukończył studia matematyczne i filozoficzne na Uniwersytecie Lwowskim. W latach 1905–1911 przebywał w Getyndze, pracując nad doktoratem pod opieką Davida Hilberta. W 1920 roku został profesorem Uniwersytetu Jana Kazimierza we Lwowie. Skupione wokół niego i Stefana Banacha grono wybitnych matematyków tworzyło silny ośrodek matematyczny specjalizujący się w analizie funkcjonalnej. Po II wojnie światowej osiedlił się we Wrocławiu, gdzie współtworzył matematyczne środowisko naukowe, a następnie wrocławską szkołę zastosowań matematyki. Jest autorem i współautorem ponad 250 prac naukowych i publikacji popularyzujących matematykę. W 1923 roku H. Steinhaus opublikował w czasopiśmie „Fundamenta Mathematicae” wyniki zawierające aksjomatyczny opis pewnej miary prawdopodobieństwa określonej na podzbiorach przestrzeni nieskończonych ciągów zero‑jedynkowych. Celem niniejszego artykułu jest próba ukazania istotnej roli, jaką wyniki te odegrały w procesie aksjomatyzacji prawdopodobieństwa, zakończonej w 1933 roku publikacją Andrieja Kołmogorowa.
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Kryteria konwergencji — dokąd zmierza Unia Europejska

100%
Bednarski T.
Studenckie Prace Prawnicze, Administratywistyczne i Ekonomiczne
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2014
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vol. 16
183 - 200
EN
The dynamics of changes in economic and social indic ators related to convergence criteria for selected Member States of the European Union is studied. Three groups of states are taken into account: states economically the strongest, southern members and the new ones, like Poland. Observance of convergence criteria for the old states of the EU is assessed and an estimation of time necessary for the new states to meet the criteria is given. An optimistic estimate of time necessary to achieve a relative economic homogeneity in the EU is 50 to 60 years. Economic and social indicators not included in the convergence criteria but essential for the economic dominance are also discussed.
3
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ON NONRESPONSE CAUSALITY TESTING IN ROTATING PANEL DESIGNS UNDER THE COX MODEL

100%
Bednarski T.
Acta Universitatis Lodziensis. Folia Oeconomica
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2014
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vol. 3
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issue 302
EN
High survey nonresponse in unemployment duration studies may have a strong effect on inference if  exit from unemployment affects the chance of nonresponse (nonresponse causality). In rotational studies  large part of the nonresponse results from panel attritions. A method to test the  presence of the causality mechanism for rotating panel designs is proposed and its asymptotic consistency is proved under the Cox regression model. An application to real labor data and a simulation study are shown.
4
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Memories of Professor Witold Klonecki

88%
Bednarski T.
Acta Universitatis Lodziensis. Folia Oeconomica
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2014
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vol. 3
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issue 302
EN
The article presents memories of Witold Klonecki.
5
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Scaled Consistent Estimation of Regression Parameters in Frailty Models

63%
Bednarski T., Skolimowska-Kulig M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2018
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vol. 5
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issue 338
133-142
PL
W artykule omówiono atrakcyjną obliczeniowo metodę estymacji parametrów dla klasy modeli regresyjnych z nieobserwowaną zmienną „frailty”. Dowiedziono, że estymator największej wiarygodności stosowany w klasycznym wykładniczym modelu regresji jest Fisherowsko zgodny z dokładnością do skali w rozważanym modelu „frailty”. Przeprowadzone badania symulacyjne oraz analiza rzeczywistych danych wskazują na dobre własności asymptotyczne prezentowanej metody estymacji.
EN
A computationally attractive method of estimation of parameters for a class of frailty regression models is discussed. The method uses maximum likelihood estimation for the classical exponential regression model. Scaled Fisher consistency is shown to hold and a simulation study indicating good asymptotic properties of the method, as well as real data case analysis, are presented.
6
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Scaled Fisher consistency for the partial likelihood estimation in various extensions of the Cox model

51%
Bednarski T., Nowak P. B., Skolimowska-Kulig M.
Statistics in Transition new series
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2022
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vol. 23
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issue 2
185-196
EN
The Cox proportional hazards model has become the most widely used procedure in survival analysis. The theoretical basis of the original model has been developed in various extensions. In the recent years, vital research has been undertaken involving the incorporation of random effects to survival models. In this setting, the random effect is a variable (frailty) which embraces a variation among individuals or groups of individuals which cannot be explained by observable covariates. The right choice of the frailty distribution is essential for an accurate description of the dependence structure present in the data. In this paper, we aim to investigate the accuracy of inference based on the primer Cox model in the existence of unobserved heterogeneity, that is, when the data generating mechanism is more complex than presumed and described by the kind of an extension of the Cox model with undefined frailty. We show that the conventional partial likelihood estimator under the considered extension is Fisher-consistent up to a scaling factor, provided symmetry-type distributional assumptions on covariates. We also present the results of simulation experiments that reveal an exemplary behaviour of the estimators.
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