Testing Nonlinearity with Rényi and Tsallis Mutual Information with an Application in the EKC Hypothesis
The nature of dependence between random variables has always been the subject of many statistical problems for over a century. Yet today, there is a great deal of research on this topic, especially focusing on the analysis of nonlinearity. Shannon mutual information has been considered to be the mos...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/1/79 |
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| author | Elif Tuna Atıf Evren Erhan Ustaoğlu Büşra Şahin Zehra Zeynep Şahinbaşoğlu |
| author_facet | Elif Tuna Atıf Evren Erhan Ustaoğlu Büşra Şahin Zehra Zeynep Şahinbaşoğlu |
| author_sort | Elif Tuna |
| collection | DOAJ |
| description | The nature of dependence between random variables has always been the subject of many statistical problems for over a century. Yet today, there is a great deal of research on this topic, especially focusing on the analysis of nonlinearity. Shannon mutual information has been considered to be the most comprehensive measure of dependence for evaluating total dependence, and several methods have been suggested for discerning the linear and nonlinear components of dependence between two variables. We, in this study, propose employing the Rényi and Tsallis mutual information measures for measuring total dependence because of their parametric nature. We first use a residual analysis in order to remove linear dependence between the variables, and then we compare the Rényi and Tsallis mutual information measures of the original data with that the lacking linear component to determine the degree of nonlinearity. A comparison against the values of the Shannon mutual information measure is also provided. Finally, we apply our method to the environmental Kuznets curve (EKC) and demonstrate the validity of the EKC hypothesis for Eastern Asian and Asia-Pacific countries. |
| first_indexed | 2024-03-09T12:50:23Z |
| format | Article |
| id | doaj.art-d7c20141a54142b4a0f38da49e07e4f8 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T12:50:23Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d7c20141a54142b4a0f38da49e07e4f82023-11-30T22:08:21ZengMDPI AGEntropy1099-43002022-12-012517910.3390/e25010079Testing Nonlinearity with Rényi and Tsallis Mutual Information with an Application in the EKC HypothesisElif Tuna0Atıf Evren1Erhan Ustaoğlu2Büşra Şahin3Zehra Zeynep Şahinbaşoğlu4Department of Statistics, Faculty of Sciences and Literature, Yildiz Technical University, Davutpasa, Esenler, 34210 Istanbul, TurkeyDepartment of Statistics, Faculty of Sciences and Literature, Yildiz Technical University, Davutpasa, Esenler, 34210 Istanbul, TurkeyDepartment of Informatics, Faculty of Management, Marmara University, Göztepe, 34180 Istanbul, TurkeyDepartment of Computer, Faculty of Engineering, Halic University, Eyupsultan, 34060 Istanbul, TurkeyDepartment of Statistics, Faculty of Sciences and Literature, Yildiz Technical University, Davutpasa, Esenler, 34210 Istanbul, TurkeyThe nature of dependence between random variables has always been the subject of many statistical problems for over a century. Yet today, there is a great deal of research on this topic, especially focusing on the analysis of nonlinearity. Shannon mutual information has been considered to be the most comprehensive measure of dependence for evaluating total dependence, and several methods have been suggested for discerning the linear and nonlinear components of dependence between two variables. We, in this study, propose employing the Rényi and Tsallis mutual information measures for measuring total dependence because of their parametric nature. We first use a residual analysis in order to remove linear dependence between the variables, and then we compare the Rényi and Tsallis mutual information measures of the original data with that the lacking linear component to determine the degree of nonlinearity. A comparison against the values of the Shannon mutual information measure is also provided. Finally, we apply our method to the environmental Kuznets curve (EKC) and demonstrate the validity of the EKC hypothesis for Eastern Asian and Asia-Pacific countries.https://www.mdpi.com/1099-4300/25/1/79nonlinearityRényi mutual informationTsallis mutual informationEKC hypothesis |
| spellingShingle | Elif Tuna Atıf Evren Erhan Ustaoğlu Büşra Şahin Zehra Zeynep Şahinbaşoğlu Testing Nonlinearity with Rényi and Tsallis Mutual Information with an Application in the EKC Hypothesis Entropy nonlinearity Rényi mutual information Tsallis mutual information EKC hypothesis |
| title | Testing Nonlinearity with Rényi and Tsallis Mutual Information with an Application in the EKC Hypothesis |
| title_full | Testing Nonlinearity with Rényi and Tsallis Mutual Information with an Application in the EKC Hypothesis |
| title_fullStr | Testing Nonlinearity with Rényi and Tsallis Mutual Information with an Application in the EKC Hypothesis |
| title_full_unstemmed | Testing Nonlinearity with Rényi and Tsallis Mutual Information with an Application in the EKC Hypothesis |
| title_short | Testing Nonlinearity with Rényi and Tsallis Mutual Information with an Application in the EKC Hypothesis |
| title_sort | testing nonlinearity with renyi and tsallis mutual information with an application in the ekc hypothesis |
| topic | nonlinearity Rényi mutual information Tsallis mutual information EKC hypothesis |
| url | https://www.mdpi.com/1099-4300/25/1/79 |
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