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You searched for subject:(Renyi correlation). Showing records 1 – 2 of 2 total matches.

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University of California – Berkeley

1. Xu, Ying. Regularization Methods for Canonical Correlation Analysis, Rank Correlation Matrices and Renyi Correlation Matrices.

Degree: Statistics, 2011, University of California – Berkeley

In multivariate analysis, canonical correlation analysis is a method that enable us to gain insight into the relationships between the two sets of variables. Itdetermines linear combinations of variables of each type with maximal correlationbetween the two linear combinations. However, in high dimensional data analysis, insufficient sample size may lead to computational problems, inconsistent estimates of parameters. In Chapter 1, three new methods of regularization are presented to improve the traditional CCA estimator in high dimensional settings. Theoretical results have been derived and the methods are evaluated using simulated data.While the linear methods are successful in many circumstances, it certainly has some limitations, especially in cases where strong nonlinear dependencies exist. In Chapter 2, I investigate some other measures of dependence, including the rank correlation and its extensions, which can capture some non-linear relationship between variables. Finally the Renyi correlation is considered in Chapter 3. I also complement my analysis with simulations that demonstrate the theoretical results.

Subjects/Keywords: Statistics; canonical correlation analysis; high dimension; rank correlation; regularization; Renyi correlation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Xu, Y. (2011). Regularization Methods for Canonical Correlation Analysis, Rank Correlation Matrices and Renyi Correlation Matrices. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/7zr9p85r

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Xu, Ying. “Regularization Methods for Canonical Correlation Analysis, Rank Correlation Matrices and Renyi Correlation Matrices.” 2011. Thesis, University of California – Berkeley. Accessed June 26, 2019. http://www.escholarship.org/uc/item/7zr9p85r.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Xu, Ying. “Regularization Methods for Canonical Correlation Analysis, Rank Correlation Matrices and Renyi Correlation Matrices.” 2011. Web. 26 Jun 2019.

Vancouver:

Xu Y. Regularization Methods for Canonical Correlation Analysis, Rank Correlation Matrices and Renyi Correlation Matrices. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2019 Jun 26]. Available from: http://www.escholarship.org/uc/item/7zr9p85r.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Xu Y. Regularization Methods for Canonical Correlation Analysis, Rank Correlation Matrices and Renyi Correlation Matrices. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/7zr9p85r

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Bowling Green State University

2. Paler, Mary Elvi Aspiras. On Modern Measures and Tests of Multivariate Independence.

Degree: PhD, Statistics, 2015, Bowling Green State University

For the last ten years, many measures and tests have been proposed for determining the independence of random vectors. This study explores the similarities and differences of some of these new measures and generalizes the properties that are suitable for measuring independence in the bivariate and multivariate case. Some of the measures that brought interest to the statistical community are Distance Correlation (dCor) by Szekely and Rizzo (2007), Maximal Information Coefficient (MIC) by Reshef, Reshef, Finucane, Grossman, McVean, Turnbaugh, Lander, Mitzenmacher and Sabeti (2011), Local Gaussian Correlation (LGC) and Global Gaussian Correlation (GGC) by Berentsen and Tjøstheim (2014), RV Coefficient by Robert and Escoufier (1976), and the HHG test statistic developed by Heller, Heller and Gorfine (2012). This study gives a state-of-the-art comparison of the measures. We compare the measures in terms of their theoretical properties. We consider the properties that are necessary and desirable for measuring dependence such as equitability and rigid motion invariance. We identify which of A. Renyi's postulates (1959) can be established or disproved for each measure. Each of the measures satisfies only two if not three properties of Renyi. Among the measures and tests explored in this paper, distance correlation is the only one that has the important characterization of being equal to zero if and only if two random variables or two random vectors are independent.Several dependence structures including linear, quadratic, cubic, exponential, sinusoid and diamond, are considered. The coefficients of the dependence measures are computed and compared for each structure. The power performance and empirical Type-I error rates of the dependence measures are also shown and compared.For detecting bivariate and multivariate association, dCov and HHG are equally powerful. Both are consistent against all dependence alternatives and the tests achieve good power for finite sample sizes. The RV coefficient is only as powerful as the two previous tests when the relationship is linear.Dependence measures are applied to real data sets concerning stocks returns and Parkinson's disease. Advisors/Committee Members: Rizzo, Maria (Advisor).

Subjects/Keywords: Statistics; Measures and Tests of Independence; Independence; Measures of Dependence; Distance covariance; Distance correlation; Global Gaussian Correlation; Maximal Information Coefficient; RV coefficient; HHG statistic; Renyi properties

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Paler, M. E. A. (2015). On Modern Measures and Tests of Multivariate Independence. (Doctoral Dissertation). Bowling Green State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1447628176

Chicago Manual of Style (16th Edition):

Paler, Mary Elvi Aspiras. “On Modern Measures and Tests of Multivariate Independence.” 2015. Doctoral Dissertation, Bowling Green State University. Accessed June 26, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1447628176.

MLA Handbook (7th Edition):

Paler, Mary Elvi Aspiras. “On Modern Measures and Tests of Multivariate Independence.” 2015. Web. 26 Jun 2019.

Vancouver:

Paler MEA. On Modern Measures and Tests of Multivariate Independence. [Internet] [Doctoral dissertation]. Bowling Green State University; 2015. [cited 2019 Jun 26]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1447628176.

Council of Science Editors:

Paler MEA. On Modern Measures and Tests of Multivariate Independence. [Doctoral Dissertation]. Bowling Green State University; 2015. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1447628176

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