A new approach for estimating the number of spikes in high-dimensional Gaussian models
Abstract
In this paper, we study the estimation of the signal subspace dimension k in a p-variate signal-plus-noise complex Gaussian model, when the noise covariance matrix is assumed to be diagonal or Toeplitz. We consider the high-dimensional asymptotic regime in which both the data dimension p and the available sample size n diverge to infinity at the same rate, while we also allow k to diverge at a slower speed. In this context, the classical estimates of the literature, consistent in the high-dimensional regime, often rely on the a priori knowledge of an upper bound k* of k, which can be misspecified in practice. Our proposed approach relies on building estimates of the tracial moments of the noise covariance matrix using the p−k* smallest eigenvalues of the sample covariance matrix (SCM), which are in turn used to build a threshold above which the k largest eigenvalues are isolated. The resulting estimate of k is proved to be consistent in the high-dimensional regime, even for the misspecified situations where k* < k. Numerical experiments in different challenging scenarios illustrate the improvement of the proposed approach over the aforementioned methods.
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BibTeX
@misc{jeannin2026approach,
title = {{A new approach for estimating the number of spikes in high-dimensional Gaussian models}},
author = {Hugo Jeannin and Pascal Vallet and Florent Bouchard and Guillaume Ginolhac and Audrey Giremus},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18059},
eprint = {2610.18059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18059},
}
RIS
TY - UNPB
TI - A new approach for estimating the number of spikes in high-dimensional Gaussian models
AU - Hugo Jeannin
AU - Pascal Vallet
AU - Florent Bouchard
AU - Guillaume Ginolhac
AU - Audrey Giremus
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18059
UR - https://arxiv.org/abs/2610.18059
AB - In this paper, we study the estimation of the signal subspace dimension k in a p-variate signal-plus-noise complex Gaussian model, when the noise covariance matrix is assumed to be diagonal or Toeplitz. We consider the high-dimensional asymptotic regime in which both the data dimension p and the available sample size n diverge to infinity at the same rate, while we also allow k to diverge at a slower speed. In this context, the classical estimates of the literature, consistent in the high-dimensional regime, often rely on the a priori knowledge of an upper bound k_* of k, which can be misspecified in practice. Our proposed approach relies on building estimates of the tracial moments of the noise covariance matrix using the p−k_* smallest eigenvalues of the sample covariance matrix (SCM), which are in turn used to build a threshold above which the k largest eigenvalues are isolated. The resulting estimate of k is proved to be consistent in the high-dimensional regime, even for the misspecified situations where k_* < k. Numerical experiments in different challenging scenarios illustrate the improvement of the proposed approach over the aforementioned methods.
ER -