A nonparametric spectral domain test of spatial isotropy

Abstract

Spectral methods have long been used for time series analysis, but their use for exploring spatially-referenced data is relatively newer and less common. Within spatial statistics the spectral representation of the spatial covariance function, the spectral density function, offers an alternative perspective of the variation of the random field. We use the spectral representation of the covariance function to develop a new method to test the assumption of spatial isotropy. The spatial isotropy spectral (SIS) test is the first to use the spectral representation of the covariance function with the primary goal of testing isotropy for geostatistical data. The SIS test is nonparametric and overcomes several deficiencies of other nonparametric tests of isotropy, such as the need for the user to make a number of choices before implementing the test. We address several challenges in using the spectral domain to construct a test statistic and develop new theory on the asymptotic distribution of the periodogram. We use a simulation study and application to investigate the utility and limitations of the SIS test. For large data sets, the SIS test is particularly useful as the computational cost is low.