T. Mrkvička, J. Dvořák, J.A. González , J. Mateu (2021)
Revisiting the random shift approach for testing in spatial statistics
Spatial Statistics 42, 100430.
Abstract
We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become a standard method for testing the independent superposition hypothesis in spatial statistics, and it is widely used in a plethora of practical applications. However, this method has a problem of liberality caused by breaking the marginal spatial correlation structure due to the toroidal correction. This indeed causes that the assumption of exchangability, which is essential for the Monte Carlo test to be exact, is not fulfilled. We present a number of permutation strategies and show that the random shift with the variance correction brings a suitable improvement compared to the torus correction in the random field case. It reduces the liberality and achieves the largest power from all investigated variants. To obtain the variance for the variance correction method, several approaches were studied. The best results were achieved, for the sample covariance as the test statistics, with the correction factor 1/n. This corresponds to the asymptotic order of the variance of the test statistics.
Keywords
Bivariate patterns, independence, random field, random shift, spatial point patterns, torus correction, variance correction