  In this paper we propose several variants to perform the independence test
between two random elements based on recurrence rates. We will show how to
calculate the test statistic in each one of these cases. From simulations we
obtain that in high dimension, our test clearly outperforms, in almost all
cases, the other widely used competitors. The test was performed on two data
sets including small and large sample sizes and we show that in both ases the
application of the test allows us to obtain interesting conclusions.
