# Large-Sample Properties of Non-Stationary Source Separation for Gaussian Signals

arXiv: https://arxiv.org/abs/2209.10176 · HTML: https://mlsanity.com/paper/2209.10176/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 50 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise](https://mlsanity.com/paper/1806.01094/) (2018)
- [Temporally Nonstationary Component Analysis; Application to Noninvasive Fetal Electrocardiogram Extraction](https://mlsanity.com/paper/2108.09353/) (2021)
- [Asymptotic and bootstrap tests for subspace dimension](https://mlsanity.com/paper/1611.04908/) (2016)
- [On the number of signals in multivariate time series](https://mlsanity.com/paper/1801.04925/) (2018)
- [A Hypothesis Testing Approach to Nonstationary Source Separation](https://mlsanity.com/paper/2105.06958/) (2021)
- [Blind source separation for non-stationary random fields](https://mlsanity.com/paper/2107.01916/) (2021)

## Abstract (arXiv)

Non-stationary source separation is a well-established branch of blind source separation with many different methods. However, for none of these methods large-sample results are available. To bridge this gap, we develop large-sample theory for NSS-JD, a popular method of non-stationary source separation based on the joint diagonalization of block-wise covariance matrices. We work under an instantaneous linear mixing model for independent Gaussian non-stationary source signals together with a very general set of assumptions: besides boundedness conditions, the only assumptions we make are that the sources exhibit finite dependency and that their variance functions differ sufficiently to be asymptotically separable. The consistency of the unmixing estimator and its convergence to a limiting Gaussian distribution at the standard square root rate are shown to hold under the previous conditions. Simulation experiments are used to verify the theoretical results and to study the impact of block length on the separation.