Determining the signal dimension in second order source separation
: Virta Joni, Nordhausen Klaus
Publisher: STATISTICA SINICA
: 2021
Statistica Sinica
: STATISTICA SINICA
: STAT SINICA
: 31
: 1
: 135
: 156
: 22
: 1017-0405
: 1996-8507
DOI: https://doi.org/10.5705/ss.202018.0347
: http://www3.stat.sinica.edu.tw/statistica/j31n1/J31N106/J31N106.html
: 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.
chi-square distribution, second order blind identification, second order stationarity, white noise
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