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

TL;DR

This paper introduces a statistical test for determining the number of white noise components in a spatial blind source separation model, providing a consistent estimator of the true dimension with improved performance over bootstrap methods.

Contribution

It develops a new asymptotic test for the latent dimension in spatial blind source separation models, including computational strategies for gridded data and a comparison with bootstrap techniques.

Findings

Test outperforms bootstrap methods in simulations

Provides a consistent estimator of the true dimension

Facilitates computations for gridded spatial data

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.