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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

Abstract

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.

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

Information

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

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

Subjects:
Primary: 62G10
Secondary: 62H20

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 2 • June, 1983
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