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Test of the Latent Dimension of a Spatial Blind Source Separation Model

Research paper by Christoph Muehlmann, François Bachoc, Klaus Nordhausen, Mengxi Yi

Indexed on: 04 Nov '20Published on: 03 Nov '20Published in: arXiv - Mathematics - Statistics



Abstract

We assume a spatial blind source separation model in which the observed multivariate spatial data is a linear mixture of latent spatially uncorrelated Gaussian 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 demonstrate that our test is at least comparable to and often outperforms bootstrap-based techniques, which are also introduced in this paper.