A geometric view on Pearson’s correlation coefficient and a generalization of it to non-linear dependencies
Abstract
Keywords
Full Text:
PDFReferences
A. Rényi, Probability Theory North-Holland Publishing Company and AkadémiaiKiadó, PublishingHouseoftheHungarianAcademyofSciences. Republished Dover USA, 2007.
C. Sabatti, Measuring dependency with volume tests, The American Statistician 56 3 (2002), 191-195. DOI: 10.1198/000313002128.
C. W. Granger, E. Maasoumi and J. Racine, A Dependence Metric for Possibly Nonlinear Processes, The Journal of Time Series Analysis 25 5 (2004),649-669.
F. Berzal, I. Blanco, D. Sanchez and M. -A. Vila, Measuring the Accuracy and Interest of Association Rules: A New Framework, Intelligent Data Analysis 6 3 (2002), 221-235.
H. Skaug and D. Tjostheim, Testing for serial independence using measures of distance between densities, P. M. Robinson and M. Rosenblatt (Eds): Athens Conference on Applied Probability and Time Series, Volume II:
Time Series Analysis In Memory of E.J. Hannan, Springer Lecture Notes in Statistics 115 (1996), 363-377.
K. Matsusita, Decision rules, based on distance, for problems of fit, two samples, and estimation, Annals of Mathematical Statistics 26 4 (1955), 631-640.
M. Studeny and J. Vejnarova, The Multiinformation Function as a Tool for Measuring Stochastic Dependence, M. I. Jordan (Eds): Learning in Graphical Models, Kluwer Academic Publishers (1998), 261-297.
M. Sugiyama and K. M. Borgwardt, Measuring Statistical Dependence via the Mutual Information Dimension, Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI’13) AAAI Press (2013), 1692-1698.
N. Balakrishnan and C. -D. Lai, Continuous Bivariate Distributions, Springer, 2009.
P. Diaconis and B. Efron, Testing for independence in a two-way table: new interpretations of Chi-square statistics, The Annals of Statistics 13 (1985), 845-874.
P. Wijayatunga, S. Mase and M. Nakamura, Appraisal of Companies with Bayesian Networks, International Journal of Business Intelligence and Data Mining 1 3 (2006), 326-346.
S. E. Fienberg and J. P. Gilbert, The Geometry of a Two by Two Contingency Table, Journal of the American Statistical Association 65 (1970), 694-701
S. Kullback and R. A. Leibler, On information and sufficiency, The Annals of Mathematical Statistics 22 1 (1951), 79-86
W. Bergsma, A bias-correction for Cramér’s V and Tschuprow’s T, Journal of the Korean Statistical Society 42 3 (2013), 323-328. http://dx.doi.org/10.1016/j.jkss.2012.10.002.
DOI: http://dx.doi.org/10.23755/rm.v30i1.5
Refbacks
- There are currently no refbacks.
Copyright (c) 2016 Priyantha Wijayatunga
This work is licensed under a Creative Commons Attribution 4.0 International License.
Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.