A CONSISTENT TEST FOR BIVARIATE DEPENDENCE

A new and consistent rank test for bivariate dependence is developed. Let X(i)' and Y(i)' denote the (approximate) normal scores associated with the iid vectors (X(i), Y(i)), i = 1, ..., n. Then the proposed test statistic may be obtained by removing the first Hajek projection from the quantity xi = n-2 SIGMA SIGMA \X(j)' - X(k)'\ . \Y(j)' - Y(k)'\. Empirical characteristic function considerations are used in our development and some related graphical methods are proposed. Some difficulties that arise in extensions to dimension k > 2 are noted. A small simulation study provides evidence of the effectiveness of the new procedure.