Powerful independence test for variables of unknown distribution I'm looking for the ideal independence test of two varaibles of unknown distribution, i.e. a non-parameteric test. Would choose between alternatives based on statistical power.
Few options that came to my mind are Kendall Tau and a test based on Spearman's rho. Chi-squared is an option, although power is a function of an additional parameter (binning), which makes it less compelling.
I wonder what other options are out there and how different options compare in terms of statistical power.
To give more color, I work in trading/finance, where forecasting relationships tend to be just as weak that it is difficult to find them. Once they are stronger, they quickly weaken to adhere to efficient market and no free lunch. 
Relationships between variable do not have to be monotonic, but continuity of conditional mean or finite number of non-nontinuities is reasonable to assume. 
We can assume iid-ness and typical sample size is 250 - 2500.
 A: You may be interested in Hoeffding's independence test, which can be calculated using the R function hoeffd in the Hmisc package, and uses a test statistic resembling that of the Crámer-von Mises goodness of fit.
The test is consistent, provided we restrict the alternative hypothesis to the case where the two variables are dependent with a continuous joint distribution function; in other words, it is "powerful" against all such alternatives, given a large enough sample.
Another possibility is to construct a contingency table by splitting the range into bins and then apply the $\chi^2$ test for independence. 
A: The test described in Heller, Heller and Gorfine (2012) detects any form of dependence and is powerful in many dependence situations. The R package to use it is 'HHG' and function 'hhg.test'. Documentation here:
https://cran.r-project.org/web/packages/HHG/HHG.pdf
Another popular method is the distance covariance by Székely and Rizzo (2009), with the R package 'energy' and function 'dcov.test'. Documentation found here:
https://cran.r-project.org/web/packages/energy/energy.pdf
