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The 2020 Election In The United States: Beta Regression Versus Regression Quantiles
Kalina, Jan
The results of the presidential election in the United States in 2020 desire a detailed statistical analysis by advanced statistical tools, as they were much different from the majority of available prognoses as well as from the presented opinion polls. We perform regression modeling for explaining the election results by means of three demographic predictors for individual 50 states: weekly attendance at religious services, percentage of Afroamerican population, and population density. We compare the performance of beta regression with linear regression, while beta regression performs only slightly better in terms of predicting the response. Because the United States population is very heterogeneous and the regression models are heteroscedastic, we focus on regression quantiles in the linear regression model. Particularly, we develop an original quintile regression map, such graphical visualization allows to perform an interesting interpretation of the effect of the demographic predictors on the election outcome on the level of individual states.
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Testing heteroscedasticity
Špaková, Mária ; Kalina, Jan (advisor) ; Zichová, Jitka (referee)
Title: Testing heteroscedasticity Author: Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jan Kalina Ph.D., Institute of Computer Science, Academy of Sciences of the Czech Republic Abstract: This paper deals with testing heteroscedasticity. It is divided into four chapters. The first three chapters focus on the theory and the last one is devoted to practical testing using specific data. In the beginning of the theoretical part, basic concepts, knowledge and relationships concerning the linear regression, the regression model and the estimation of parameters by the method of ordinary least squares are introduced. The rest of this part is devoted to heteroskedasticity, its consequences and solutions. The following heteroscedasticity tests are being discussed: Breusch - Pagan, Goldfeld - Quandt and White. The practical part contains actual applications of the described tests and other methods to detect heteroskedasticity using three examples: Outlays vs. income, GDP and Expenditures on food. The aim of this paper is to discuss the above-mentioned tests. Three examples on real data with economic motivation confirm the theoretical properties of the tests. A uniformly optimal test of heteroscedasticity does not exist and different tests yield rather different...
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Various Approaches to Szroeter’s Test for Regression Quantiles
Kalina, Jan ; Peštová, B.
Regression quantiles represent an important tool for regression analysis popular in econometric applications, for example for the task of detecting heteroscedasticity in the data. Nevertheless, they need to be accompanied by diagnostic tools for verifying their assumptions. The paper is devoted to heteroscedasticity testing for regression quantiles, while their most important special case is commonly denoted as the regression median. Szroeter’s test, which is one of available heteroscedasticity tests for the least squares, is modified here for the regression median in three different ways: (1) asymptotic test based on the asymptotic representation for regression quantiles, (2) permutation test based on residuals, and (3) exact approximate test, which has a permutation character and represents an approximation to an exact test. All three approaches can be computed in a straightforward way and their principles can be extended also to other heteroscedasticity tests. The theoretical results are expected to be extended to other regression quantiles and mainly to multivariate quantiles.
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Various Approaches to Szroeter’s Test for Regression Quantiles
Kalina, Jan ; Peštová, Barbora
Regression quantiles represent an important tool for regression analysis popular in econometric applications, for example for the task of detecting heteroscedasticity in the data. Nevertheless, they need to be accompanied by diagnostic tools for verifying their assumptions. The paper is devoted to heteroscedasticity testing for regression quantiles, while their most important special case is commonly denoted as the regression median. Szroeter’s test, which is one of available heteroscedasticity tests for the least squares, is modified here for the regression median in three different ways: (1) asymptotic test based on the asymptotic representation for regression quantiles, (2) permutation test based on residuals, and (3) exact approximate test, which has a permutation character and represents an approximation to an exact test. All three approaches can be computed in a straightforward way and their principles can be extended also to other heteroscedasticity tests. The theoretical results are expected to be extended to other regression quantiles and mainly to multivariate quantiles.
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Exact Inference In Robust Econometrics under Heteroscedasticity
Kalina, Jan ; Peštová, B.
The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also the asymptotic behavior of the permutation test statistics of the Goldfeld-Quandt and Breusch-Pagan tests is investigated. A numerical experiment on real economic data is presented, which also shows how to perform a robust prediction model under heteroscedasticity. Theoretical results may be simply extended to the context of multivariate quantiles
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Exact Inference In Robust Econometrics under Heteroscedasticity
Kalina, Jan ; Peštová, Barbora
The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also the asymptotic behavior of the permutation test statistics of the Goldfeld-Quandt and Breusch-Pagan tests is investigated. A numerical experiment on real economic data is presented, which also shows how to perform a robust prediction model under heteroscedasticity. Theoretical results may be simply extended to the context of multivariate quantiles
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Testing heteroscedasticity
Špaková, Mária ; Kalina, Jan (advisor) ; Zichová, Jitka (referee)
Title: Testing heteroscedasticity Author: Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jan Kalina Ph.D., Institute of Computer Science, Academy of Sciences of the Czech Republic Abstract: This paper deals with testing heteroscedasticity. It is divided into four chapters. The first three chapters focus on the theory and the last one is devoted to practical testing using specific data. In the beginning of the theoretical part, basic concepts, knowledge and relationships concerning the linear regression, the regression model and the estimation of parameters by the method of ordinary least squares are introduced. The rest of this part is devoted to heteroskedasticity, its consequences and solutions. The following heteroscedasticity tests are being discussed: Breusch - Pagan, Goldfeld - Quandt and White. The practical part contains actual applications of the described tests and other methods to detect heteroskedasticity using three examples: Outlays vs. income, GDP and Expenditures on food. The aim of this paper is to discuss the above-mentioned tests. Three examples on real data with economic motivation confirm the theoretical properties of the tests. A uniformly optimal test of heteroscedasticity does not exist and different tests yield rather different...
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On Exact Heteroscedasticity Testing for Robust Regression
Kalina, Jan ; Peštová, Barbora
The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also the asymptotic behavior of the permutation test statistics of the Goldfeld-Quandt and Breusch-Pagan tests is investigated. A numerical experiment on real economic data is presented, which also shows how to perform a robust prediction model under heteroscedasticity.
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Modeling development of incurred value of claim
Kantorová, Petra ; Zimmermann, Pavel (advisor) ; Hrevuš, Jan (referee)
This diploma project is focused on the estimation of incurred value of claim and probability of the claim remaining opened (not settled) in the specific stage of the insurance settlement process. The change of incurred value of claim means the change of settlement process stage. Generalized linear model is used for modelling these changes. Classical linear regression model also belongs into this theory, which is its special case, just with stricter premises. Generalized linear model among others allows solving the problem of heteroscedasticity in the unusual way using joint model. This model is applied in the practical part of this piece of work. Logistic regression is the part of the generalized linear model theory, which helps to model the probability of the claim remaining opened in this piece of work. The model outcome is presented in graphic way, especially the graphs containing probability that levels of given claim will occur in certain range.
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