Some multivariate goodness-of-fit tests based on data depth

Based on data depth, three types of nonparametric goodness-of-fit tests for multivariate distribution are proposed in this paper. They are Pearson’s chi-square test, tests based on EDF and tests based on spacings, respectively. The Anderson--Darling (AD) test and the Greenwood test for bivariate normal distribution and uniform distribution are simulated. The results of simulation show that these two tests have low type I error rates and become more efficient with the increase in sample size. The AD-type test performs more powerfully than the Greenwood type test.