Shrinkage MMSE estimators of covariances beyond the zero-mean and stationary variance assumptions - Université Claude Bernard Lyon 1
Conference Papers Year : 2024

Shrinkage MMSE estimators of covariances beyond the zero-mean and stationary variance assumptions

Abstract

We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/highvariance empirical estimate with a biased regularization estimator, striking a bias-variance trade-off. Literature provides optimal settings of the regularization amount through risk minimization between the true covariance and its shrunk counterpart. Such estimators were derived for zero-mean statistics with i.i.d. diagonal regularization matrices accounting for the average sample variance solely. We extend these results to regularization matrices accounting for the sample variances both for centered and noncentered samples. In the latter case, the empirical estimate of the true mean is incorporated into our shrinkage estimators. Introducing confidence weights into the statistics also enhance estimator robustness against outliers. We compare our estimators to other shrinkage methods both on numerical simulations and on real data to solve a detection problem in astronomy.
Fichier principal
Vignette du fichier
shrinkage_eusipco_2024_reviewed.pdf (16.72 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04693522 , version 1 (10-09-2024)

Identifiers

  • HAL Id : hal-04693522 , version 1

Cite

Olivier Flasseur, Éric Thiébaut, Loïc Denis, Maud Langlois. Shrinkage MMSE estimators of covariances beyond the zero-mean and stationary variance assumptions. EUSIPCO 2024, Aug 2024, Lyon, France. ⟨hal-04693522⟩
0 View
0 Download

Share

More