  Nonparametric rank tests for homogeneity and component independence are
proposed, which are based on data compressors. For homogeneity testing the idea
is to compress the binary string obtained by ordering the two joint samples and
writing 0 if the element is from the first sample and 1 if it is from the
second sample and breaking ties by randomization (extension to the case of
multiple samples is straightforward). $H_0$ should be rejected if the string is
compressed (to a certain degree) and accepted otherwise. We show that such a
test obtained from an ideal data compressor is valid against all alternatives.
Component independence is reduced to homogeneity testing by constructing two
samples, one of which is the first half of the original and the other is the
second half with one of the components randomly permuted.
