On the Power of Some Nonparametric Isotropy Tests

In this paper, properties of nonparametric significance tests verifying the random field isotropy hypothesis are discussed. In particular, the subject of the conducted analysis is the probability of rejecting the null hypothesis when it is true. A potential significant difference of empirical rejection probability from the assumed significance level could distort the results of statistical inference. The tests proposed by Guan, Sherman, Calvin (2004) and Lu, Zimmerman (2005) are considered. A simulation study has been carried out through generating samples from a given theoretical distribution and repeatedly testing the null hypothesis. Isotropic distributions are considered, among others, those based on a multidimensional normal distribution. The main aim of the paper is to compare both considered nonparametric significance tests verifying the random field isotropy hypothesis. For this purpose, the empirical rejection probabilities for both tests have been calculated and compared with the assumed significance level.