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.
"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