Refereed journal article or data article (A1)
Determining the signal dimension in second order source separation
List of Authors: Virta Joni, Nordhausen Klaus
Publisher: STATISTICA SINICA
Publication year: 2021
Journal: Statistica Sinica
Journal name in source: STATISTICA SINICA
Journal acronym: STAT SINICA
Volume number: 31
Issue number: 1
Start page: 135
End page: 156
Number of pages: 22
ISSN: 1017-0405
eISSN: 1996-8507
DOI: http://dx.doi.org/10.5705/ss.202018.0347
URL: http://www3.stat.sinica.edu.tw/statistica/j31n1/J31N106/J31N106.html
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/52801750
Despite being an important topic in practice, estimating the number of non-noise components in blind source separation has received little attention in the literature. Recently, two bootstrap-based techniques for estimating the dimension were proposed; however, although very efficient, they suffer from long computation times as a result of the resampling. We approach the problem from a large-sample viewpoint, and develop an asymptotic test and a corresponding consistent estimate for the true dimension. Our test statistic based on second-order temporal information has a very simple limiting distribution under the null hypothesis, and requires no parameters to estimate. Comparisons with resampling-based estimates show that the asymptotic test provides comparable error rates, with significantly faster computation times. Lastly, we illustrate the method by applying it to sound recording data.
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