Large-sample properties of non-stationary source separation for Gaussian signals
: Bachoc, Francois; Muehlmann, Christoph; Nordhausen, Klaus; Virta, Joni
Publisher: Institute of Mathematical Statistics
: CLEVELAND
: 2024
: Electronic Journal of Statistics
: ELECTRONIC JOURNAL OF STATISTICS
: ELECTRON J STAT
: 18
: 1
: 2241
: 2291
: 51
: 1935-7524
DOI: https://doi.org/10.1214/24-EJS2252
: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-18/issue-1/Large-sample-properties-of-non-stationary-source-separation-for-Gaussian/10.1214/24-EJS2252.full
: https://research.utu.fi/converis/portal/detail/Publication/457272648
: https://arxiv.org/abs/2209.10176
Non-stationary source separation isa well-established branch of blind source separation with many different methods. However, for none of these methods large-sample results are available. To bridge this gap, we develop large-sample theory for NSS-JD, a popular method of non-stationary source separation based on the joint diagonalization of block-wise covariance matrices. We work under an instantaneous linear mixing model for independent Gaussian non-stationary source signals together with a very general set of assumptions: besides boundedness conditions, the only assumptions we make are that the sources exhibit finite dependency and that their variance functions differ sufficiently to be asymptotically separable. The consistency of the unmixing estimator and its convergence to a limiting Gaussian distribution at the standard square root rate are shown to hold under the previous conditions. Simulation experiments are used to verify the theoretical results and to study the impact of block length on the separation.
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The work of FB was supported by the Project GAP (ANR-21-CE40-0007) of the French National Research Agency (ANR). The work of CM and KN was supported by the Austrian Science Fund P31881-N32. The work of JV was supported by the Research Council of Finland, Grants 335077, 347501 and 353769.
