Consistent distribution-free $K$-sample and independence tests for univariate random variables

Understand

A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data.

• The partition size matters, and the optimal partition size is data dependent.
• While for detecting simple relationships coarse partitions may be best, for detecting complex relationships a great gain in power can be achieved by considering finer partitions.
• We suggest novel consistent distribution-free tests that are based on summation or maximization aggregation of scores over all partitions of a fixed size.