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2024-02-18
00:07
Beyond the Erdős–Sós conjecture
Davoodi, Akbar ; Piguet, Diana ; Řada, Hanka ; Sanhueza-Matamala, N.
We prove an asymptotic version of a tree-containment conjecture of Klimošová, Piguet and Rozhoň [European J. Combin. 88 (2020), 103106] for graphs with quadratically many edges. The result implies that the asymptotic version of the Erdős-Sós conjecture in the setting of dense graphs is correct.

Úplný záznam
2024-01-25
22:11
From John Graunt to Adolphe Quetelet: on the Origins Of Demography
Kalina, Jan
John Graunt (1620-1674) and Adolphe Quetelet (1796-1874) were two important personalities, who contributed to the origins of demography. As they both developed statistical techniques for the analysis of demographic data, they are important also from the point of view of history of statistics. The contributions of both Graunt and Quetelet especially to the development of mortality tables and models are recalled in this paper. Already from the 17th century, the available mortality tables were exploited for computing life annuities. Also the contribution of selected personalities inspired by Graunt are recalled here, the work of Christian Huygens, Jacob Bernoulli, or Abraham de Moivre is discussed to document that the historical development of statistics and probability theory was connected with the development of demography.

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2024-01-25
22:11
The 2022 Election in the United States: Reliability of a Linear Regression Model
Kalina, Jan ; Vidnerová, Petra ; Večeř, M.
In this paper, the 2022 United States election to the House of Representatives is analyzed by means of a linear regression model. After the election process is explained, the popular vote is modeled as a response of 8 predictors (demographic characteristics) on the state-wide level. The main focus is paid to verifying the reliability of two obtained regression models, namely the full model with all predictors and the most relevant submodel found by hypothesis testing (with 4 relevant predictors). Individual topics related to assessing reliability that are used in this study include confidence intervals for predictions, multicollinearity, and also outlier detection. While the predictions in the submodel that includes only relevant predictors are very similar to those in the full model, it turns out that the submodel has better reliability properties compared to the full model, especially in terms of narrower confidence intervals for the values of the popular vote.

Úplný záznam
2024-01-25
22:11
Some Robust Approaches to Reducing the Complexity of Economic Data
Kalina, Jan
The recent advent of complex (and potentially big) data in economics requires modern and effective tools for their analysis including tools for reducing the dimensionality (complexity) of the given data. This paper starts with recalling the importance of Big Data in economics and with characterizing the main categories of dimension reduction techniques. While there have already been numerous techniques for dimensionality reduction available, this work is interested in methods that are robust to the presence of outlying measurements (outliers) in the economic data. Particularly, methods based on implicit weighting assigned to individual observations are developed in this paper. As the main contribution, this paper proposes three novel robust methods of dimension reduction. One method is a dimension reduction within a robust regularized linear regression, namely a sparse version of the least weighted squares estimator. The other two methods are robust versions of feature extraction methods popular in econometrics: robust principal component analysis and robust factor analysis.

Úplný záznam
2024-01-25
22:11
DC 5.3 Odhady kovariancí odhadnutého pole koncentrací
Brabec, Marek ; Malý, Marek ; Malá, Ivana
BIBLIOGRAFICKÉ ÚDAJE: Výzkumná zpráva č. SS02030031-V95. Praha: ICS CAS, 2023. 22 s. ANOTACE: Obsahem tohoto dokumentu je popis výsledku typu O: SS02030031-V95, Odhady kovariancí odhadnutého prostorového pole koncentrací. Jde o postup odhadu kovariančních parametrů jak samotného latentního Gaussovského prostorového pole, tak o odhad kovariance regresních parametrů v modelu. Dále též formulace modelu malého měřítka vybraného z dříve testovaných variant. Testování algoritmu optimalizace umístění stanic na předvybraném scénáři.

Úplný záznam
2024-01-25
22:10
Epidemiologické modely s agenty
Neruda, Roman
Tento příspěvek je jemným úvodem do problematiky agentních modelů a jejich aplikací v epidemiologickém modelování. Představíme agentní modely jednak z hlediska informatiky, jednak jako nástroj modelování v jiných vědních disciplínách. V příkladové studii ukážeme model s agenty a sociální sítí jejich kontaktů, který slouží pro simulaci vývoje epidemie a vlivu protiepidemických opatření.

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2023-12-17
00:02

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2023-12-06
00:37
The Equation |x| - |Ax| = b
Rohn, Jiří
We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant.
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Úplný záznam
2023-12-06
00:37
Globální implicitní funkce
Rohn, Jiří
Tento text pochází z roku 1973 a nebyl dosud zveřejněn. Jeho hlavním výsledkem je věta o existenci a jednoznačnosti globální implicitní funkce v Rn. Tomuto výsledku předchází řada pomocných tvrzení.
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Úplný záznam
2023-08-06
00:02

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