Abstract: We assume a spatial blind source separation model in which the observed multivariate spatial data are a linear mixture of latent spatially uncorrelated random fields containing a number of pure white noise components. We propose a test on the number of white noise components, and obtain the asymptotic distribution of its statistic for a general domain. We also demonstrate how computations can be facilitated in the case of gridded observation locations. Based on this test, we obtain a consistent estimator of the true dimension. Simulation studies and an environmental application provided in the Supplementary Material demonstrate that our test is at least comparable to, and often outperforms bootstrap-based techniques.

Key words and phrases: Asymptotic distribution, kernel function, multivariate spatial data, signal number, spatial bootstrap.