2024-03-10
03:13 |
Fractionally Isomorphic Graphs and Graphons
Hladký, Jan ; Hng, Eng Keat
Fractional isomorphism is a well-studied relaxation of graph isomorphism with a very rich theory. Grebík and Rocha [Combinatorica 42, pp 365–404 (2022)] developed a concept of fractional isomorphism for graphons and proved that it enjoys an analogous theory. In particular, they proved that if two sequences of graphs that are fractionally isomorphic converge to two graphons, then these graphons are fractionally isomorphism. Answering the main question from ibid, we prove the converse of the statement above: If we have two fractionally isomorphic graphons, then there exist sequences of graphs that are fractionally isomorphic converge and converge to these respective graphons. As an easy but convenient corollary of our methods, we get that every regular graphon can be approximated by regular graphs.
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2024-03-10
03:13 |
Permutation Flip Processes
Hladký, Jan ; Řada, Hanka
We introduce a broad class of stochastic processes on permutations which we call flip processes. A single step in these processes is given by a local change on a randomly chosen fixed-sized tuple of the domain. We use the theory of permutons to describe the typical evolution of any such flip process started from any initial permutation. More specifically, we construct trajectories in the space of permutons with the property that if a finite permutation is close to a permuton then for any time it stays with high probability is close to this predicted trajectory. This view allows to study various questions inspired by dynamical systems.
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2024-03-10
03:13 |
Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results
Kalina, Jan
The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions of common statistical methods for every statistical modeling task and the most habitually used (“vanilla”) versions may yield rather misleading results in nonstandard situations. Linear regression is considered here as the most fundamental econometric model. First, the analysis of a world tourism dataset is presented, where the number of international arrivals is modeled for 140 countries of the world as a response of 14 pillars (indicators) of the Travel and Tourism Competitiveness Index. Heteroscedasticity is clearly recognized in the dataset. However, the Aitken estimator, which would be the standard remedy in such a situation, is revealed here to be very inappropriate, regression quantiles represent a much more suitable solution here. The second illustration with artificial data reveals standard regression quantiles to be unsuitable for data contaminated by outlying values, their recently proposed robust version turns out to be much more appropriate. Both illustrations reveal that choosing suitable methods represent an important (and often difficult) part of the analysis of economic data.
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2024-02-18
00:07 |
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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.
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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.
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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.
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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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