Multidimensional plots and precedence tests for point processes on

Given two univariate distributions F and G , the hypothesis that F = G can be tested against the alternative that F < G using a precedence test statistic, or more generally the procentile–procentile plot of G against F . In this paper we propose a d -dimensional generalization of the p – p plot that can be used to construct a precedence test of F = G against the alternative that F ≺ G for various stochastic orders on ℜ d . The p – p plot process is shown to converge to a Gaussian limit. Under the null hypothesis, the p – p plot can be regarded as a two sample version of the empirical copula process. In one dimension, the test statistics proposed correspond to classical nonparametric rank-based tests.