Transformed empirical processes and modified Kolmogorov-Smirnov tests for multivariate distributions
多元分布的变换经验过程与修正 Kolmogorov–Smirnov 检验
A general way of constructing classes of goodness-of-fit tests for multivariate samples is presented. These tests are based on a random signed measure that plays the same role as the empirical process in the construction of the classical Kolmogorov-Smirnov tests. The resulting tests are consistent against any fixed alternative, and, for each sequence of contiguous alternatives, a test in each class can be chosen so as to optimize the discrimination of those alternatives.