Test of the Latent Dimension of a Spatial Blind Source Separation Model
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866913309036380160 |
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| author | Muehlmann, Christoph Bachoc, François Nordhausen, Klaus Yi, Mengxi |
| author_facet | Muehlmann, Christoph Bachoc, François Nordhausen, Klaus Yi, Mengxi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_01711 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Test of the Latent Dimension of a Spatial Blind Source Separation Model Muehlmann, Christoph Bachoc, François Nordhausen, Klaus Yi, Mengxi Statistics Theory 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. |
| title | Test of the Latent Dimension of a Spatial Blind Source Separation Model |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2011.01711 |