I'd like to test the hypothesis that there is a monotonic relationship between two variables, without assuming a specific model. What is the most robust (i.e. lowest probability of type-II error) way to do this?
I can think of a few options:
use a linear model of untransformed data. It'll be robust enough, even if I don't think the true relationship is linear.
look at rank-transformed data, e.g. with Spearman's rank correlation coefficient
use some kind of resampling approach, in which the order of the dependent variable is randomly shuffled. I'm not sure what statistic to compare in this approach.
Is there a fairly standard approach to this problem?