Abstract: An ideal independence test should possess three properties: it should be zero-independence equivalent, numerically efficient, and asymptotically normal. We introduce a slicing procedure for estimating a popular measure of nonlinear dependence, leading to the resultant sliced independence test simultaneously possessing all three properties. In addition, the power performance of the sliced independence test improves as the number of observations within each slice increases. The popular rank test corresponds to a special case of the sliced independence test that contains two observations within each slice. The sliced independence test is thus more powerful than the rank test. The size performance of the sliced independence test is insensitive to the number of slices, in that the slicing estimation is consistent and asymptotically normal for a wide range of slice numbers. We further adapt the sliced independence test to account for the presence of multivariate control variables. The theoretical properties are confirmed using comprehensive simulations and an application to an astronomical data set.

Key words and phrases: Correlation, measure of association, rank tests.