  Pearson's Chi-squared test, though widely used for detecting association
between categorical variables, exhibits low statistical power in large sparse
contingency tables. To address this limitation, two novel permutation tests
have been recently developed: the distance covariance permutation test and the
U-statistic permutation test. Both leverage the distance covariance functional
but employ different estimators. In this work, we explore key statistical
properties of the distance covariance for categorical variables. Firstly, we
show that unlike Chi-squared, the distance covariance functional is B-robust
for any number of categories (fixed or diverging). Second, we establish the
strong consistency of distance covariance screening under mild conditions, and
simulations confirm its advantage over Chi-squared screening, especially for
large sparse tables. Finally, we derive an approximate null distribution for a
bias-corrected distance correlation estimate, demonstrating its effectiveness
through simulations.
