Open Access
June, 1983 Graph-Theoretic Measures of Multivariate Association and Prediction
Jerome H. Friedman, Lawrence C. Rafsky
Ann. Statist. 11(2): 377-391 (June, 1983). DOI: 10.1214/aos/1176346148


Interpoint-distance-based graphs can be used to define measures of association that extend Kendall's notion of a generalized correlation coefficient. We present particular statistics that provide distribution-free tests of independence sensitive to alternatives involving non-monotonic relationships. Moreover, since ordering plays no essential role, the ideas are fully applicable in a multivariate setting. We also define an asymmetric coefficient measuring the extent to which (a vector) $X$ can be used to make single-valued predictions of (a vector) $Y$. We discuss various techniques for proving that such statistics are asymptotically normal. As an example of the effectiveness of our approach, we present an application to the examination of residuals from multiple regression.


Download Citation

Jerome H. Friedman. Lawrence C. Rafsky. "Graph-Theoretic Measures of Multivariate Association and Prediction." Ann. Statist. 11 (2) 377 - 391, June, 1983.


Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0528.62052
MathSciNet: MR696054
Digital Object Identifier: 10.1214/aos/1176346148

Primary: 62G10
Secondary: 62H20

Keywords: examination of residuals , graph theory , interpoint distances , linear permutation statistics , Multivariate association

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 2 • June, 1983
Back to Top