Determining the signal dimension in second order source separation

Joni Virta, Klaus Nordhausen

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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.
Original languageEnglish
Pages (from-to)135-156
JournalStatistica Sinica
Publication statusPublished - 2021
MoE publication typeA1 Journal article-refereed


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