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Journal of the American Statistical Association Volume 94, 1999 - Issue 445
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Theory and Method

Data-Driven Rank Tests for Independence

Wilbert C. M. Kallenberg Faculty of Applied Mathematics, University of Twente, 7500 AE, Enschede, The Netherlands
&
Teresa Ledwina Institute of Mathematics, Polish Academy of Sciences, 51–617, Wroclaw, Poland
Pages 285-301 | Received 01 Mar 1997, Published online: 17 Feb 2012
 
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Abstract

We introduce new rank tests for testing independence. The new testing procedures are sensitive not only for grade linear correlation, but also for grade correlations of higher-order polynomials. The number of polynomials involved is determined by the data. Model selection is combined with application of the score test in the selected model. Whereas well-known tests as Spearman's test or Hoeffding's test may completely break down for alternatives that are dependent but have low grade linear correlation, the new tests have greater power stability. Monte Carlo results clearly show this behavior. Theoretical support is obtained by proving consistency of the new tests.

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