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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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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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Kellyho kritérium a Bayesovská statistika
Pardubický, Štěpán ; Večeř, Jan (vedoucí práce) ; Kalina, Jan (oponent)
Klasickým problémem investora je hledání výhodných investičních příležitostí. Jak by se měl však investor zachovat, pokud takovou příležitost nalezne? Na tuto otázku odpovídá Kellyho kritérium, nesoucí jméno po americkém vědci J.L.Kellym. Kritérium při opakovaných sázkách maximalizuje asymptotickou exponenciální míru růstu kapitálu, čehož docílí maximalizací střední hodnoty logaritmické užitkové funkce. Kritérium před- pokládá fixní názor investora na skutečné pravděpodobnostní rozdělení. V praxi však není jasné, jak by měl být tento názor utvořen. V této práci zkombinujeme Kellyho kritérium s bayesovským přístupem, který umožní namísto fixního názoru uvažovat názorů více a nechat je validovat vývojem kapitálu. Na závěr aplikujeme získané poznatky na situaci investora na binomickém trhu. 1
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Robust regularized regression
Krett, Jakub ; Kalina, Jan (vedoucí práce) ; Maciak, Matúš (oponent)
Táto práca sa venuje predstaveniu rôznych typov robustných a regularizovaných re- gresných odhadov. Cieľom práce je predstavenie nového odhadu LWS-lasso, ktorý kom- binuje robustnosť a regularizáciu zároveň. Najprv sa v práci vysvetlia základné pojmy z lineárnej regresie a modifikácie odhadu najmenších štvorcov. Potom sa predstavia rôzne robustné a regularizované odhady spolu s novým odhadom LWS-lasso a jeho softvérovou implementáciou. Následne sa vybrané odhady navzájom porovnajú na reálnych dátach a v simulačnej štúdii. 1
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Robustní regrese a robustní neuronové sítě
Janáček, Patrik ; Kalina, Jan (vedoucí práce) ; Maciak, Matúš (oponent)
Klasická metoda nejmenších čtverců v lineární regresi je náchylná na přítomnost od- lehlých hodnot v datech. Cílem této práce je představit několik robustních alternativ metody nejmenších čtverců v rámci lineární regrese a diskutovat jejich vlastnosti. Ná- sleduje představení robustních neuronových sítí inspirovaných těmito odhady, které jsou porovnány v rámci simulační studie. Slibnou se jeví zejména metoda nejmenších váže- ných čtverců v kombinaci s adaptivními váhami, která je schopna kombinovat vysokou robustnost s efektivitou při absenci kontaminace v datech. 1
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A Bootstrap Comparison of Robust Regression Estimators
Kalina, Jan ; Janáček, Patrik
The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more preferable alternatives. It has been repeatedly recommended to use the least squares together with a robust estimator, where the latter is understood as a diagnostic tool for the former. In other words, only if the robust estimator yields a very different result, the user should investigate the dataset closer and search for explanations. For this purpose, a hypothesis test of equality of the means of two alternative linear regression estimators is proposed here based on nonparametric bootstrap. The performance of the test is presented on three real economic datasets with small samples. Robust estimates turn out not to be significantly different from non-robust estimates in the selected datasets. Still, robust estimation is beneficial in these datasets and the experiments illustrate one of possible ways of exploiting the bootstrap methodology in regression modeling. The bootstrap test could be easily extended to nonlinear regression models.
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Recent Trends in Machine Learning with a Focus on Applications in Finance
Kalina, Jan ; Neoral, Aleš
Machine learning methods penetrate to applications in the analysis of financial data, particularly to supervised learning tasks including regression or classification. Other approaches, such as reinforcement learning or automated machine learning, are not so well known in the context of finance yet. In this paper, we discuss the advantages of an automated data analysis, which is beneficial especially if a larger number of datasets should be analyzed under a time pressure. Important types of learning include reinforcement learning, automated machine learning, or metalearning. This paper overviews their principles and recalls some of their inspiring applications. We include a discussion of the importance of the concept of information and of the search for the most relevant information in the field of mathematical finance. We come to the conclusion that a statistical interpretation of the results of theautomatic machine learning remains crucial for a proper understanding of the knowledge acquired by the analysis of the given (financial) data.
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On kernel-based nonlinear regression estimation
Kalina, Jan ; Vidnerová, P.
This paper is devoted to two important kernel-based tools of nonlinear regression: the Nadaraya-Watson estimator, which can be characterized as a successful statistical method in various econometric applications, and regularization networks, which represent machine learning tools very rarely used in econometric modeling. This paper recalls both approaches and describes their common features as well as differences. For the Nadaraya-Watsonestimator, we explain its connection to the conditional expectation of the response variable. Our main contribution is numerical analysis of suitable data with an economic motivation and a comparison of the two nonlinear regression tools. Our computations reveal some tools for the Nadaraya-Watson in R software to be unreliable, others not prepared for a routine usage. On the other hand, the regression modeling by means of regularization networks is much simpler and also turns out to be more reliable in our examples. These also bring unique evidence revealing the need for a careful choice of the parameters of regularization networks
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Application Of Implicitly Weighted Regression Quantiles: Analysis Of The 2018 Czech Presidential Election
Kalina, Jan ; Vidnerová, P.
Regression quantiles can be characterized as popular tools for a complex modeling of a continuous response variable conditioning on one or more given independent variables. Because they are however vulnerable to leverage points in the regression model, an alternative approach denoted as implicitly weighted regression quantiles have been proposed. The aim of current work is to apply them to the results of the second round of the 2018 presidential election in the Czech Republic. The election results are modeled as a response of 4 demographic or economic predictors over the 77 Czech counties. The analysis represents the first application of the implicitly weighted regression quantiles to data with more than one regressor. The results reveal the implicitly weighted regression quantiles to be indeed more robust with respect to leverage points compared to standard regression quantiles. If however the model does not contain leverage points, both versions of the regression quantiles yield very similar results. Thus, the election dataset serves here as an illustration of the usefulness of the implicitly weighted regression quantiles.
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Application Of Implicitly Weighted Regression Quantiles: Analysis Of The 2018 Czech Presidential Election
Kalina, Jan ; Vidnerová, Petra
Regression quantiles can be characterized as popular tools for a complex modeling of a continuous response variable conditioning on one or more given independent variables. Because they are however vulnerable to leverage points in the regression model, an alternative approach denoted as implicitly weighted regression quantiles have been proposed. The aim of current work is to apply them to the results of the second round of the 2018 presidential election in the Czech Republic. The election results are modeled as a response of 4 demographic or economic predictors over the 77 Czech counties. The analysis represents the first application of the implicitly weighted regression quantiles to data with more than one regressor. The results reveal the implicitly weighted regression quantiles to be indeed more robust with respect to leverage points compared to standard regression quantiles. If however the model does not contain leverage points, both versions of the regression quantiles yield very similar results. Thus, the election dataset serves here as an illustration of the usefulness of the implicitly weighted regression quantiles.
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