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Biometrika 1987 74(4):887-890; doi:10.1093/biomet/74.4.887
© 1987 by Biometrika Trust
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MISCELLANEA

A nonparametric correlation coefficient and a two-sample test for random vectors or directions

P. E. JUPP

Department of Statistics, University of St. Andrews St. Andrews KY16 9SS, U.K.

For multivariate or directional data a nonparametric correlation coefficient and a two-sample statistic are proposed. Both of these statistics are coordinate-free, resistant and unchanged under almost all small perturbations of the data. The correlation coefficient generalizes Kendall's tau and the angular-angular correlation coefficient of Fisher & Lee (1982). The two-sample statistic is related to the Cramér-von Mises statistic and to Watson's (1962) U2. A numerical example is given.

Key Words: Correlation • Directional data • Robust • U-statistic


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