Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation
Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distingui...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Berentsen, Geir Drage [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Statistics and computing - Springer US, 1991, 24(2013), 5 vom: 06. Juni, Seite 785-801 |
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| Übergeordnetes Werk: |
volume:24 ; year:2013 ; number:5 ; day:06 ; month:06 ; pages:785-801 |
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| DOI / URN: |
10.1007/s11222-013-9402-8 |
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OLC2033746399 |
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| 520 | |a Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of $\mathbb{R}^{2}$, and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection. | ||
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10.1007/s11222-013-9402-8 doi (DE-627)OLC2033746399 (DE-He213)s11222-013-9402-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Berentsen, Geir Drage verfasserin aut Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of $\mathbb{R}^{2}$, and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection. Independence testing Local dependence Local Gaussian correlation Dependence map Tjøstheim, Dag aut Enthalten in Statistics and computing Springer US, 1991 24(2013), 5 vom: 06. Juni, Seite 785-801 (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:24 year:2013 number:5 day:06 month:06 pages:785-801 https://doi.org/10.1007/s11222-013-9402-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4126 AR 24 2013 5 06 06 785-801 |
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10.1007/s11222-013-9402-8 doi (DE-627)OLC2033746399 (DE-He213)s11222-013-9402-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Berentsen, Geir Drage verfasserin aut Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of $\mathbb{R}^{2}$, and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection. Independence testing Local dependence Local Gaussian correlation Dependence map Tjøstheim, Dag aut Enthalten in Statistics and computing Springer US, 1991 24(2013), 5 vom: 06. Juni, Seite 785-801 (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:24 year:2013 number:5 day:06 month:06 pages:785-801 https://doi.org/10.1007/s11222-013-9402-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4126 AR 24 2013 5 06 06 785-801 |
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10.1007/s11222-013-9402-8 doi (DE-627)OLC2033746399 (DE-He213)s11222-013-9402-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Berentsen, Geir Drage verfasserin aut Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of $\mathbb{R}^{2}$, and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection. Independence testing Local dependence Local Gaussian correlation Dependence map Tjøstheim, Dag aut Enthalten in Statistics and computing Springer US, 1991 24(2013), 5 vom: 06. Juni, Seite 785-801 (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:24 year:2013 number:5 day:06 month:06 pages:785-801 https://doi.org/10.1007/s11222-013-9402-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4126 AR 24 2013 5 06 06 785-801 |
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10.1007/s11222-013-9402-8 doi (DE-627)OLC2033746399 (DE-He213)s11222-013-9402-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Berentsen, Geir Drage verfasserin aut Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of $\mathbb{R}^{2}$, and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection. Independence testing Local dependence Local Gaussian correlation Dependence map Tjøstheim, Dag aut Enthalten in Statistics and computing Springer US, 1991 24(2013), 5 vom: 06. Juni, Seite 785-801 (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:24 year:2013 number:5 day:06 month:06 pages:785-801 https://doi.org/10.1007/s11222-013-9402-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4126 AR 24 2013 5 06 06 785-801 |
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Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of $\mathbb{R}^{2}$, and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection. © Springer Science+Business Media New York 2013 |
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Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of $\mathbb{R}^{2}$, and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection. © Springer Science+Business Media New York 2013 |
| abstract_unstemmed |
Abstract It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of $\mathbb{R}^{2}$, and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection. © Springer Science+Business Media New York 2013 |
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Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation |
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