JSM 2005 Online Program

Abstract #303274

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Activity Number:	277
Type:	Contributed
Date/Time:	Tuesday, August 9, 2005 : 10:30 AM to 12:20 PM
Sponsor:	Section on Nonparametric Statistics
Abstract - #303274
Title:	The General Definition and Utility of Correlation Coefficients
Author(s):	Rudy Gideon*+
Companies:	University of Montana
Address:	Dept of Math Sc, Missoula, MT, 59812, United States
Keywords:	correlation ; regression ; greatest deviation ; gini ; Kendall ; Spearman
Abstract:	Previous attempts at defining other correlation measures mostly tried to generalize the inner product definition used in Pearson's correlation coefficient. This does not allow for certain useful correlations such as the Greatest Deviation or Gini's. In this work, the idea in Gideon and Hollister (1987) of seeing correlation as the difference between distance from perfect negative and perfect positive correlation will be used to bring together a general setting. Pearson, Spearman, and Kendall correlation coefficients are then seen as special cases where a linear restriction holds. It also will be seen how to define a wide variety of correlation coefficients. A method and an example of simple linear regression with these correlations is given in a general setting as an example of the utility of any correlation coefficient. The general focus of this work is simply to outline notation and concepts necessary for using any correlation coefficient as an estimating function. This general method leads to estimation by any correlation coefficient in advanced areas such as general linear models and time series.

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