Statistical tests consistent under any alternative are provided for both goodness-of-fit and two-sample comparisons. They are based on (1) the derivation of estimates for the tails of the probability distribution of some particular functionals of a Wiener sheet and (2) the use of a mapping that carries normalized empirical processes (asymptotically distributed as Brownian bridge) onto new processes that converge in distribution to a Wiener sheet. The proposed test statistics are easily obtained from the data. Hints for its computation and empirical estimations of the power of the tests are given.
Alejandra Cabana. Enrique M. Cabana. "Goodness-of-Fit and Comparison Tests of the Kolmogorov-Smirnov Type for Bivariate Populations." Ann. Statist. 22 (3) 1447 - 1459, September, 1994. https://doi.org/10.1214/aos/1176325636