Determining the signal dimension in second order source separation

Abstract

While an important topic in practice, the estimation of 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, and although very efficient, they suffer from the long computation times caused by the resampling. We approach the problem from a large sample viewpoint and develop an asymptotic test 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 to the resampling-based estimates show that the asymptotic test provides comparable error rates with significantly faster computation time. An application to sound recording data is used to illustrate the method in practice.

Figures (5)

• Figure 1: Estimating $k$ by divide-and-conquer in Setting D1.
• Figure 2: Estimating $k$ by divide-and-conquer in Setting D2.
• Figure 3: Estimating $k$ by divide-and-conquer in Setting D3.
• Figure 4: The 20-variate sound data time series.
• Figure 5: The three estimated sound signals based on SOBI6.

Theorems & Definitions (12)

• Proposition 1
• Lemma 1
• Lemma 2
• Corollary 1
• Lemma 3
• Lemma 4
• proof : Proof of Lemma \ref{['lem:0']}
• proof : Proof of Lemma \ref{['lem:1']}
• proof : Proof of Corollary \ref{['cor:1']}
• proof : Proof of Lemma \ref{['lem:2']}