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Miscellany

Test of multivariate linear models using spatial concordances

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Pages 167-183 | Received 01 May 2002, Accepted 01 Jun 2004, Published online: 31 Jan 2007
 

Abstract

Kendall’s τ for univariate samples is extended to the multivariate case using unit direction vectors in place of signs. Depending on whether the design matrix is fixed, this statistic yields a test for the multivariate analysis of variance or multivariate regression. Tests of independence based on this statistic are easy, efficient, and robust. Its asymptotic properties and its Pitman efficiency are studied. In addition, some useful algebra in multiple dimensions is presented.

Acknowledgement

This work was supported by Research Fund NSF-DMS-00-71757.

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