Using data compressors to construct order tests for homogeneity and component independence

Nonparametric order tests for homogeneity and component independence are proposed, which are based on data compressors. For homogeneity testing the idea is to compress the word obtained by ordering the combined samples and writing the number of the sample in the place of each element. H₀ 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.