On the basis of independent and identically distributed bivariate random vectors, where the components are categorial and continuous variables, respectively, the related concomitants, also called induced order statistic, are considered. The main theoretical result is a functional central limit theorem for the empirical process of the concomitants in a triangular array setting. A natural application is hypothesis testing. An independence test and a two-sample test are investigated in detail. The fairly general setting enables limit results under local alternatives and bootstrap samples. For the comparison with existing tests from the literature simulation studies are conducted. The empirical results obtained confirm the theoretical findings.
The authors wish to thank the two Referees for very helpful comments and suggestions which improved the paper significantly. Special thanks goes to the Associate Editor who drew the attention of the authors to the work of Chatterjee .
"Empirical process of concomitants for partly categorial data and applications in statistics." Bernoulli 28 (2) 803 - 829, May 2022. https://doi.org/10.3150/21-BEJ1367