Virta, Joni; Nordhausen, Klaus Determining the signal dimension in second order source separation. (English) Zbl 1464.62227 Stat. Sin. 31, No. 1, 135-156 (2021). Summary: 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. Cited in 1 Document MSC: 62F03 Parametric hypothesis testing 62F12 Asymptotic properties of parametric estimators 60H40 White noise theory Keywords:asymptotic test; blind source separation; chisquare distribution; second-order blind identification; second-order stationarity; white noise Software:R; tsBSS; BSSasymp; JADE PDFBibTeX XMLCite \textit{J. Virta} and \textit{K. Nordhausen}, Stat. Sin. 31, No. 1, 135--156 (2021; Zbl 1464.62227) Full Text: arXiv References: [1] Belouchrani, A., Abed Meraim, K., Cardoso, J.-F. and Moulines, E. (1997). A blind source separation technique based on second order statistics.IEEE Transactions on Signal Processing 45, 434-444. [2] Chang, J., Guo, B. and Yao, Q. (2018). Principal component analysis for second-order stationary vector time series.The Annals of Statistics46, 2094-2124. · Zbl 1454.62255 [3] Comon, P. and Jutten, C. (2010).Handbook of Blind Source Separation. 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[26] E-mail: joni.virta@utu.fi [27] Klaus Nordhausen [28] Vienna University of Technology, Institute of Statistics & Mathematical Methods in Economics, [29] Wiedner Hauptstr. 8-10 1040 Vienna, Austria. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.