Test of the Latent Dimension of a Spatial Blind Source Separation Model
Muehlmann, C., Bachoc, F., Nordhausen, K., & Yi, M. (2024). Test of the Latent Dimension of a Spatial Blind Source Separation Model. Statistica Sinica, 34(2), Early online. https://doi.org/10.5705/ss.202021.0326
Published inStatistica Sinica
© Institute of Statistical Science, Academia Sinica
We assume a spatial blind source separation model in which the observed multivariate spatial data is 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 in the Supplemental Material demonstrate that our test is at least comparable to and often outperforms bootstrap-based techniques, which are also introduced in this paper.
PublisherInstitute of Statistical Science, Academia Sinica
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Additional information about fundingThe work of Christoph Muehlmann, Klaus Nordhausen and Mengxi Yi are supported by the Austrian Science Fund (No. P31881-N32). The work of Mengxi Yi is also supported by the National Natural Science Foundation of China (No. 12101119).
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